> > Static Analysis Problems

Static Analysis Problems
This chapter contains static analysis problems and Structure's results. In a Static analysis, Structure calculates deformations, stresses, and strains on your model in response to specified loads and subject to specified constraints. Structure also automatically calculates all predefined measures. This list of measures differs based on the analysis type.
This chapter contains the following models:
mvss001: 2D Axisymmetric Cylindrical Shell
mvss002: 2D Axisymmetric Flat Circular Plate
mvss003: 2D Plane Stress Cantilever Plate
mvss004: 2D Plane Strain Thick-Walled Cylinder
mvss005: 2D Axisymmetric Thick-Walled Cylinder
mvss006: 3D Cantilever Beam
mvss007: 3D Beam with Multiple Constraints
mvss008: 3D Beam with Parallelogram-Shaped Shell Elements
mvss009: 3D Beam with Trapezoidal-Shaped Shell Elements
mvss010: 3D Curved Beam Modeled with Shells
mvss011: 3D Simply Supported Rectangular Plate
mvss012: 3D Clamped Rectangular Plate
mvss013: 3D Hemispherical Shell
mvss015: 3D Scordelis-Lo Roof
mvss016: 2D Axisymmetric Cylinder/Sphere
mvss017: 2D Tapered Membrane with Gravity Load
mvss018: 3D Z-Section Cantilevered Plate
mvss019: 3D Cylindrical Shell with Edge Moment
mvss020: Beam Sections
mvss021:Thick-Walled Cylinder Under Internal Pressure
mvss022: Thin-Walled Spherical Vessel Under Its Own Weight
mvsl001: Static Analysis of Composite Lay-up
mvss001: 2D Axisymmetric Cylindrical Shell
 Analysis Type: Static Model Type: 2D Axisymmetric Comparison: NASTRAN No. V2411 Reference: • P.E. Grafton and D.R. Strome, "Analysis of Axisymmetrical Shells by the Direct Stiffness Method," AIAA Journal, 1(10): 2342-2347. • J.W. Jones and H.H. Fong, "Evaluation of NASTRAN," Structural Mechanics Software Series, Vol. IV (N. Perrone and W. Pilkey, eds.), 1982. Description: Find the radial deflection at the loaded end of a cantilever cylinder that is modeled axisymmetrically.
 Element B is optional, but has been included here to increase the accuracy of results in the area local to the loaded end and to reduce computation time.
Specifications
 Element Type: 2D shell (2) Units: IPS Dimensions: length: 6radius: 5thickness: 0.01 Material Properties: Mass Density: 0Cost Per Unit Mass: 0Young's Modulus: 1e7 Poisson's Ratio: 0.3Thermal Expansion: 0Conductivity: 0 Constraint: placed on point A: fixed in all DOF Load: placed on point C: FX = 1Distribution: N/ASpatial Variation: N/A
Comparison of Results Data
 Theory MSC/ NASTRAN Structure % Difference Radial Deflection @ Load (a=disp_x_radial) 2.8769e-3 2.8715e-3 2.8725e-3 0.15% Convergence %: 0.5% on Local Disp and SE Max P: 7 No. Equations: 33
mvss002: 2D Axisymmetric Flat Circular Plate
 Analysis Type: Static Model Type: 2D Axisymmetric Comparison: ANSYS No. 15 Reference: Timoshenko, S. Strength of Materials, Part II, Advanced Theory and Problems. 3rd ed. NY: D. Van Nostrand Co., Inc. 1956, pp. 96, 97, and 103. Description: A flat circular plate, modeled axisymmetrically, is subjected to various edge constraints and surface loadings. Determine the maximum stress for each case.
Specifications
 Element Type: 2D shell (1) Units: IPS Dimensions: radius: 40thickness: 1 Material Properties: Mass Density: 0Cost Per Unit Mass: 0Young's Modulus: 3e7 Poisson's Ratio: 0.3Thermal Expansion: 0Conductivity: 0
 Constraints: Location Degrees of Freedom clamped placed on point B: fixed in all DOF simple placed on point B: fixed in TransX and TransY
 Loads: Location/Magnitude: Distribution: Spatial Variation: clamped placed on edge A-B: FY = 6 per unit area uniform simple placed on edge A-B: FY = 1.5 per unit area uniform
Comparison of Results Data
 Theory ANSYS Structure % Difference Maximum Stress (m=max_prin_mag, a=clamped) 7200 7152 7200 0.0% Convergence %: 0.0% on Local Disp and SE Max P: 5 No. Equations: 15 Maximum Stress (m=max_prin_mag, a=simple) 2970 2989 29701 0.0% Convergence %: 0.0% on Local Disp and SE Max P: 5 No. Equations: 16
1 Sign of result is dependent upon direction of load.
mvss003: 2D Plane Stress Cantilever Plate
 Analysis Type: Static Model Type: 2D Plane Stress Comparison: NASTRAN No. V2408A Reference: Singer, Ferdinand L. Strength of Materials. Harper & Row, 1962, Art. 52, p. 133. Description: Find the bending stress at the fixed end for a cantilever plate subjected to an in-plane shear load.
Specifications
 Element Type: 2D plate (1) Units: IPS Dimensions: length: 3height: 0.6thickness: 0.1 Material Properties: Mass Density: 0Cost Per Unit Mass: 0Young's Modulus: 1.07e7 Poisson's Ratio: 0Thermal Expansion: 0Conductivity: 0 Constraints: placed on edge A-B: fixed in TransX, TransY Loads: placed on edge C-D: FY= –200Distribution: per unit lengthSpatial Variation: uniform The theoretical results are based on elementary beam theory. Structure models the actual physical structure, capturing the singular stresses present at the constrained corners. Setting Poisson's ratio equal to zero reduces the model to its elementary form.
Comparison of Results Data
 Theory MSC/ NASTRAN Structure % Difference Bending Stress @ Node A (m=max_stress_xx) 6.0e4 5.5190e4 6.0121e4 0.20% Convergence %: 0.0% on Local Disp and SE Max P: 4 No. Equations: 22
mvss004: 2D Plane Strain Thick-Walled Cylinder
 Analysis Type: Static Model Type: 2D Plane Strain Comparison: The MacNealHarder Accuracy Tests Reference: MacNeal, R.H., and Harder, R.L. "A Proposed Standard Set of Problems to Test Finite Element Accuracy." Finite Elements in Analysis and Design I. Elsevier Science Publishers, 1985. Description: A thick-walled cylinder, modeled symmetrically, is loaded with unit internal pressure. Find the radial displacement at the inner radius for two nearly incompressible materials.
Specifications
 Element Type: 2D solid (1) Units: IPS Dimensions: outer radius: 9.0inner radius: 3.0 Material Properties: Mass Density: 0Cost Per Unit Mass: 0Young's Modulus: 1000 Poisson's Ratio:• 0.49 (case 1)• 0.499 (case 2) Constraints (UCS): placed on edges A-B & C-D:fixed in all DOF except TransR Loads: placed on edge A-D: pressure load = 1Distribution: N/ASpatial Variation: uniform
Comparison of Results Data
 Theory Structure % Difference Radial Displacement @ Inner Radius (case 1) (m=rad_disp) 5.0399e-3 5.0394e-3 <0.01% Convergence %:1% on Local Disp and SE Max P: 6 No. Equations: 38 Radial Displacement @ Inner Radius (case 2) (m=rad_disp) 5.0602e-3 5.0553e-3 0.09% Convergence %: 1.0% on Local Disp and SE Max P: 6 No. Equations: 38
mvss005: 2D Axisymmetric Thick-Walled Cylinder
 Analysis Type: Static Model Type: 2D Axisymmetric Comparison: NASTRAN No. V2410 Reference: Crandall S.H., Dahl N.C. , and Larnder T.J. An Introduction to the Mechanics of Solids. 2nd ed. NY: McGraw-Hill Book Co., 1972, pp. 293-297. Description: Find the stress at radii r = 6.5" and r = 11.5". A thick-walled cylinder is modeled axisymmetrically and subjected to internal pressure.
Specifications
 Element Type: 2D solid (3) Units: IPS Dimensions: inner radius: 6height: 8thickness: 6 Material Properties: Mass Density: 0Cost Per Unit Mass: 0Young's Modulus: 3e7 Poisson's Ratio: 0Thermal Expansion: 0Conductivity: 0 Constraints (UCS): placed on edges A-D & B-C: fixed in TransY and RotZ Loads: placed on edge A-B: pressure load = 10Distribution: per unit areaSpatial Variation: uniform
Comparison of Results Data
 Theory MSC/ NASTRAN Structure % Difference @ r = 6.5 Stress Radial (m=r6_5_radial) -8.03 -8.05 -7.9720 0.72% Stress Hoop (m=r6_5_hoop) 14.69 14.73 14.69 0.0% @ r = 11.5 Stress Radial (m=r11_5_radial) -0.30 -0.30 -2.6636e-1 0.0% Stress Hoop (m=r11_5_hoop) 6.96 6.96 6.96 0.0% Convergence %: 0.25% on Local Disp and SE Max P: 4 No. Equations: 54
mvss006: 3D Cantilever Beam
 Analysis Type: Static Model Type: 3D Comparison: NASTRAN No. V2405 Reference: Roark, R.J., and Young, W.C. Formulas for Stress and Strain. NY: McGraw-Hill Book Co., 1982, p. 96. Description: A cantilever beam is subjected to a load at the free end. Find the deflection at the free end and the bending stress at the fixed end.
Specifications
 Element Type: beam (1) Units: IPS Dimensions: length: 30 Beam Properties: Area: 0.310IYY: 0.0241Shear FY: 1000 1CY: 0.5 J: 0.0631IZZ: 0.0390Shear FZ: 1000 1CZ: 0.375 Material Properties: Mass Density: 0Cost Per Unit Mass: 0Young's Modulus: 1.0e7 Poisson's Ratio: 0.3Thermal Expansion: 0Conductivity: 0 Constraints: placed on point A: fixed in all DOF Loads: placed on point B: FY = 100Distribution: N/ASpatial Variation: N/A
1 Structure beams consider shear; however, the represented theoretical problem does not. The values for shear factor compensate for this.
Comparison of Results Data
 Theory MSC/ NASTRAN Structure % Difference Deflection @ Tip (m=max_disp_y) 2.3077 2.3077 2.3094 0.073% Bending Stress @ Fixed End (m=max_beam_bending) 38461 38461 38461 0.0% Convergence %: 0.0% on Local Disp and SE Max P: 4 No. Equations: 24
mvss007: 3D Beam with Multiple Constraints
 Analysis Type: Static Model Type: 3D Comparison: ANSYS No. 2 Reference: Timoshenko, S. Strength of Materials, Part I, Elementary Theory and Problems. 3rd ed. NY: D. Van Nostrand Co., Inc., 1955, p. 98, Problem 4. Description: A standard 30" WF beam, supported as shown below, is loaded on the overhangs uniformly. Find the maximum bending stress and deflection at the middle of the beam.
Specifications
 Element Type: beam (4) Units: IPS Dimensions: length: 480 Beam Properties: Area: 50.65IYY: 1Shear FY: 0.8333CY: 15 J: 7893IZZ: 7892Shear FZ: 0.8333CZ: 15 Material Properties: Mass Density: 0Cost Per Unit Mass: 0Young's Modulus: 3e7 Poisson's Ratio: 0.3Thermal Expansion: 0Conductivity: 0
 Constraints Location Degrees of Freedom placed on point B:placed on point D: fixed in all DOF except RotY and RotZfixed in TransY and TransZ
 Loads Location/Magnitude Distribution Spatial Variation placed on edge A-B: FY = 833.33placed on edge D-E: FY = 833.33 per unit lengthper unit length uniformuniform
Comparison of Results Data
 Theory ANSYS Structure % Difference Max Bending Stress @ Middle (m=max_beam_bending) 11400 11404 11403.91 0.03% Max Deflection @ Middle (m=disp_center) 0.182 0.182 0.182 0.0% Convergence %: 0.0% on Local Disp and SE Max P: 4 No. Equations: 96
mvss008: 3D Beam with Parallelogram-Shaped Shell Elements
 Analysis Type: Static Model Type: 3D Comparison: The MacNealHarder Accuracy Tests Reference: MacNeal, R.H., and Harder, R.L. "A Proposed Standard Set of Problems to Test Finite Element Accuracy." Finite Elements in Analysis and Design I. Elsevier Science Publishers, 1985. Description: A straight cantilever beam, constructed of parallelogram-shaped elements, is subjected to four different unit loads at the free end, including• extension• in-plane shear• out-of-plane shear• twisting loadsFind the tip displacement in the direction of the load for each case.
Specifications
 Element Type: shell (3) Units: IPS Dimensions: length: 6width: 0.2thickness: 0.1 Material Properties: Mass Density: 0Cost Per Unit Mass: 0Young's Modulus: 1e7 Poisson's Ratio: 0.3Thermal Expansion: 0Conductivity: 0 Constraints: placed on edge A-D: fixed in all DOF
 Loads: Location/Magnitude: Distribution: Spatial Variation: extension placed on edge B-C: FX = 1 total load uniform in_plane placed on edge B-C: FY = 1 total load uniform out_plane placed on edge B-C: FZ = 1 total load uniform twist placed on point E: MX = 1 total load N/A
Comparison of Results Data
 Theory Structure % Difference Tip Disp. in Direction of Load (l=extension, m=max_disp_x) 3e-5 2.998e-5 0.06% Tip Disp. in Direction of Load (l=in_plane, m=max_disp_y) 0.1081 0.1078 0.27% Tip Disp. in Direction of Load (l=out_plane, m=max_disp_z) 0.4321 0.4309 0.27% Tip Disp. in Direction of Load (l=twist, m=max_rot_x) 0.03408 1 0.03424 0.46% Convergence %: 0.9% on Local Disp and SE Max P: 6 No. Equations: 396
1 There is a typographical error in Table 3 (p. 10) of MacNeal-Harder for the twist load on a straight beam. It should read 0.03408.
mvss009: 3D Beam with Trapezoidal-Shaped Shell Elements
 Analysis Type: Static Model Type: 3D Comparison: The MacNealHarder Accuracy Tests Reference: MacNeal, R.H., and Harder, R.L. "A Proposed Standard Set of Problems to Test Finite Element Accuracy." Finite Elements in Analysis and Design I. Elsevier Science Publishers, 1985. Description: A straight cantilever beam, constructed of trapezoidal-shaped elements, is subjected to four different unit loads at the free end, including• extension• in-plane shear• out-of-plane shear• twistingFind the tip displacement in the direction of the load for each case.
Specifications
 Element Type: shell (3) Units: IPS Dimensions: length: 6width: 0.2thickness: 0.1 Material Properties: Mass Density: 0Cost Per Unit Mass: 0Young's Modulus: 1e7 Poisson's Ratio: 0.3Thermal Expansion: 0Conductivity: 0 Constraints: placed on edge A-D: fixed in all DOF
 Loads: Location/Magnitude: Distribution: Spatial Variation: extension placed on edge B-C: FX = 1 total load uniform in_plane placed on edge B-C: FY = 1 total load uniform out_plane placed on edge B-C: FZ = 1 total load uniform twist placed on point E: MX = 1 total load N/A
Comparison of Results Data
 Theory Structure % Difference Tip Disp. in Direction of Load(l=extension, m=max_disp_x) 3e-5 2.998e-5 0.08% Tip Disp. in Direction of Load(l=in_plane, m=max_disp_y) 0.1081 0.1079 0.32% Tip Disp. in Direction of Load(l=out_plane, m=max_disp_z) 0.4321 .4311 0.23% Tip Disp. in Direction of Load(l=twist, m=max_rot_x) 0.03408 1 0.03381 0.79% Convergence %: 0.7% on Local Disp and SE Max P: 6 No. Equations: 906
1 There is a typographical error in Table 3 (p. 10) of the McNeal-Harder reference for the twist load on a straight beam. It should read 0.03408.
mvss010: 3D Curved Beam Modeled with Shells
 Analysis Type: Static Model Type: 3D Comparison: The MacNealHarder Accuracy Tests Reference: MacNeal, R.H., and Harder, R.L. "A Proposed Standard Set of Problems to Test Finite Element Accuracy." Finite Elements in Analysis and Design I. Elsevier Science Publishers, 1985. Description: A curved beam, spanning a 90arc, is fixed at one end and free at the other. If the beam is subjected to in-plane and out-of-plane loads at the free end, find the tip displacement in the direction of the load for both cases.
Specifications
 Element Type: shell (2) Units: IPS Dimensions: outer radius: 4.32inner radius: 4.12thickness: 0.1 Material Properties: Mass Density: 0Cost Per Unit Mass: 0Young's Modulus: 1e7 Poisson's Ratio: 0.25Thermal Expansion: 0Conductivity: 0 Constraints: placed on edge A-D: fixed in all DOF
 Loads: Location/Magnitude: Distribution: Spatial Variation: in_plane placed on edge B-C: FY = 1 total load uniform out_plane placed on edge B-C: FZ = 1 total load uniform
Comparison of Results Data
 Theory Structure % Difference Tip Displacement in Direction of Load(l=in_plane, m=tip_disp_y) 0.08734 0.08833 1.13% Tip Displacement in Direction of Load(l=out_plane, m=tip_disp_z) 0.5022 0.50057 0.32% Convergence %: 0.3% on Local Disp and SE Max P: 6 No. Equations: 234
mvss011: 3D Simply Supported Rectangular Plate
 Analysis Type: Static Model Type: 3D Comparison: The MacNealHarder Accuracy Tests Reference: MacNeal, R.H., and Harder, R.L. "A Proposed Standard Set of Problems to Test Finite Element Accuracy." Finite Elements in Analysis and Design I. Elsevier Science Publishers, 1985. Description: A flat plate is simply supported on all four edges. One quarter of the plate is modeled using symmetry. The plate is loaded with two different loads, including uniform pressure and a point load at the center. Find the displacement at the center of the plate.
Specifications
 Element Type: shell (2) Units: IPS Dimensions: length: 5width: 1thickness: 0.0001 Material Properties: Mass Density: 0Cost Per Unit Mass: 0Young's Modulus: 1.7472e7 Poisson's Ratio: 0.3Thermal Expansion: 0Conductivity: 0
 Constraints Location Degrees of Freedom placed on edges A-D, C-D:placed on edge A-B:placed on edge B-C: fixed in TransX, TransY, and TransZfixed in TransY, RotX, and RotZfixed in TransX, RotY, and RotZ
 Loads: Location/Magnitude: Distribution: Spatial Variation: pressure placed on all shells:pressure = 1e4 total load per unit area uniform point placed on B: FZ = 1e4 N/A N/A
Comparison of Results Data
 Theory Structure % Difference Displacement @ Center(l=pressure, m=disp_z_cen) –12.97 –12.97 0.0% Displacement @ Center(l=point, m=disp_z_cen) 16.96 16.81 0.88% Convergence %: 0.8% on Local Disp and SE Max P: 9 No. Equations: 438
mvss012: 3D Clamped Rectangular Plate
 Analysis Type: Static Model Type: 3D Comparison: The MacNealHarder Accuracy Tests Reference: MacNeal, R.H., and Harder, R.L. "A Proposed Standard Set of Problems to Test Finite Element Accuracy." Finite Elements in Analysis and Design I. Elsevier Science Publishers, 1985. Description: One quarter of a rectangular plate, clamped on four edges, is modeled using symmetry. The plate is loaded with two different loads, including uniform pressure and a point load at center. Find the displacement at the center of the plate.
Specifications
 Element Type: shell (2) Units: IPS Dimensions: length: 5width: 1thickness: 0.0001 Material Properties: Mass Density: 0Cost Per Unit Mass: 0Young's Modulus: 1.7472e7 Poisson's Ratio: 0.3Thermal Expansion: 0Conductivity: 0
 Constraints Location Degrees of Freedom placed on edges A-D, D-C:placed on edge A-B:placed on edge B-C: fixed in all DOFfixed in TransY, RotX, and RotZfixed in TransX, RotY, and RotZ
 Loads: Location/Magnitude: Distribution: Spatial Variation: pressure placed on all shells:pressure = 1e4 per unit area uniform point placed on B: FZ = 1e4 N/A N/A
Comparison of Results Data
 Theory Structure % Difference Displacement @ Center(l=pressure, m=measure1) –2.56 –2.604 1.71% Displacement @ Center(l=point, m=measure1) 7.23 7.168 0.85% Convergence %: 1.3% on Local Disp and SE Max P: 9 No. Equations: 625
mvss013: 3D Hemispherical Shell
 Analysis Type: Static Model Type: 3D Comparison: The MacNealHarder Accuracy Tests Reference: MacNeal, R.H., and Harder, R.L. "A Proposed Standard Set of Problems to Test Finite Element Accuracy." Finite Elements in Analysis and Design I. Elsevier Science Publishers, 1985. Description: One quarter of an open hemisphere is modeled with symmetry and loaded with alternating point loads at 90 intervals on the equator. Find the radial displacement at any load point.
Specifications
 Element Type: shell (4) Units: IPS Dimensions:(using a one-quarter model) radius: 10arc span: 90othickness: 0.04 Material Properties: Mass Density: 0Cost Per Unit Mass: 0Young's Modulus: 6.825e7 Poisson's Ratio: 0.3Thermal Expansion: 0Conductivity: 0
 Constraints Location Degrees of Freedom placed on curve A-C:placed on curve G-E:placed on point D fixed in TransP, RotR, and RotTfixed in TransP, RotR, and RotTfixed in TransT
 Loads: Location/Magnitude: Distribution: Spatial Variation placed on point C: FR = 1placed on E: FR = 1 N/AN/A N/AN/A
Comparison of Results Data
 Theory Structure % Difference Radial Displacement @ Load(m=disp_rad) –0.0924 –0.0933 0.97% Convergence %: 0.6% on Local Disp and SE Max P: 9 No. Equations: 1965
mvss014: 3D Cantilever Beam Twisted by 90
 Analysis Type: Static Model Type: 3D Comparison: The MacNealHarder Accuracy Tests Reference: MacNeal, R.H., and Harder, R.L. "A Proposed Standard Set of Problems to Test Finite Element Accuracy." Finite Elements in Analysis and Design I. Elsevier Science Publishers, 1985. Description: A cantilever beam, twisted by 90, is subjected to in-plane and out-of-plane loads at the free end. Find the tip displacement in the direction of the load for each case.
Specifications
 Element Type: solid (2) Units: IPS Dimensions: length: 12width: 1.1thickness: 0.32angle of twist 90o (from fixed to free end) Material Properties: Mass Density: 0Cost Per Unit Mass: 0Young's Modulus: 29e6 Poisson's Ratio: 0.22Thermal Expansion: 0Conductivity: 0 Constraints: placed on root surface: fixed in all DOF
 Loads: Location/Magnitude: Distribution: Spatial Variation: in_plane placed on free end surface: FY = 1 total load uniform out_plane placed on free end surface: FZ = 1 total load uniform
Comparison of Results Data
 Theory Structure % Difference Tip Displacement in Direction of Load(l=in_plane, m=disp_tip_y1) 0.005424 0.005428 0.73% Tip Displacement in Direction of Load(l=out_of_plane, m=disp_tip_z1) 0.001754 0.001760 0.342% Convergence %: 0.8% on Local Disp and SE Max P: 5 No. Equations: 590
mvss015: 3D Scordelis-Lo Roof
 Analysis Type: Static Model Type: 3D Comparison: The MacNealHarder Accuracy Tests Reference: MacNeal, R.H., and Harder, R.L. "A Proposed Standard Set of Problems to Test Finite Element Accuracy." Finite Elements in Analysis and Design I. Elsevier Science Publishers, 1985. Description: A Scordelis-Lo roof is one-quarter of an arched roof modeled using symmetry and loaded uniformly. Find the vertical displacement at the midpoint of the straight side (of the whole roof).
Specifications
 Element Type: shell (1) Units: IPS Dimensions:(using a one-quarter model) length: 25radius: 25arc span: 40othickness: 0.25 Material Properties: Mass Density: 0Cost Per Unit Mass: 0Young's Modulus: 4.32e8 Poisson's Ratio: 0Thermal Expansion: 0Conductivity: 0
 Constraints Location Degrees of Freedom (UCS)(UCS)(UCS) placed on curve A-B:placed on curve A-D:placed on curve C-D fixed in TransZ, RotR, and RotTfixed in TransT, RotZ, and RotRfixed in TransR and TransT
 Loads: Location/Magnitude: Distribution: Spatial Variation: placed on face A-B-C-D: FZ = 90 per unit area uniform
Comparison of Results Data
 Theory Structure % Difference Vertical Displacement @ Point B(m=disp_z_mid) –0.3024 –0.3008 0.53% Convergence %: 0.2% on Local Disp and SE Max P: 7 No. Equations: 148
mvss016: 2D Axisymmetric Cylinder/Sphere
 Analysis Type: Static Model Type: 2D Axisymmetric Reference: NAFEMS, LSB1, No. IC 39 Description: An axisymmetric cylinder and half-sphere vessel is loaded with uniform internal pressure. Find the hoop stress on the outer surface at point D.
Specifications
 Element Type: 2D shell (4) Units: MKS Dimensions: radius: 1thickness: 0.025 Material Properties: Mass Density: 0.007Cost Per Unit Mass: 0Young's Modulus: 210000 Poisson's Ratio: 0.3Thermal Expansion: 0Conductivity: 0
 Constraints Location Degrees of Freedom constraint1 placed on point A:placed on point E: fixed in TransX and RotZfixed in TransY
 Loads: Location/Magnitude: load1 placed on all 2D shell elements: internal pressure = 1
Comparison of Results Data
 Theory Structure1 % Difference Szz on outer surface 38.5 38.62 0.3% Convergence %: 0.8% on Local Disp and SE Max P: 7 No. Equations: 72
1 You cannot view the results information in the summary file. To view the results, you must define a result window for the Stress ZZ (Bottom), and query the value at point D.
mvss017: 2D Tapered Membrane with Gravity Load
 Analysis Type: Static Model Type: Plane Stress Reference: NAFEMS, LSB1, No. IC 2 Description: A tapered membrane has uniform acceleration in the global X direction. Find the direct stress Sxx at point B.
Specifications
 Element Type: 2D plate (2) Units: MKS Dimensions: thickness: 0.1 Material Properties: Mass Density: 0.007Cost Per Unit Mass: 0Young's Modulus: 210000 Poisson's Ratio: 0.3Thermal Expansion: 0Conductivity: 0
 Constraints: Location Degrees of Freedom constraint1 placed on curves A-B, B-C:placed on point B: fixed in TransXfixed in TransX, TransY
Comparison of Results Data
 Theory Structure % Difference Stress XX at point B(m=measure1) 0.247 0.247 0% Convergence %: 0.7% on Local Disp and SE Max P: 7 No. Equations: 248
mvss018: 3D Z-Section Cantilevered Plate
 Analysis Type: Static Model Type: 3D Reference: NAFEMS, LSB1, No. IC 29 Description: A Z-section cantilevered plate is subjected to a torque at the free end by two uniformly distributed edge shears. Find the direct stress Sxx at the mid-plane of the plate.
Specifications
 Element Type: shell (6) Units: MKS Dimensions: length: 10thickness: 0.1 Material Properties: Mass Density: 0.007Cost Per Unit Mass: 0Young's Modulus: 210000 Poisson's Ratio: 0.3Thermal Expansion: 0Conductivity: 0
 Constraints Location Degrees of Freedom constraint1 placed on curves A-B, B-C, and C-D: fixed in TransX, TransY, and TransZ
Comparison of Results Data
 Theory Structure1 % Difference Sxx at mid-surface at point M –108.8 –110.02 1.1% Convergence %: 0.4% on Local Disp and SE Max P: 7 No. Equations: 870
1 You cannot view the results information in the summary file. To view the results, you must define a result window for the measure Stress XX (Top and Bottom), and query the value at point M. Then average the top (118) and bottom (105.56) values.
mvss019: 3D Cylindrical Shell with Edge Moment
 Analysis Type: Static Model Type: 3D Reference: NAFEMS, LSB1, No. IC 19 Description: A cylindrical shell in 3D space is loaded with a uniform normal edge moment on one edge. Find the outer surface tangential stress at point E.
Specifications
 Element Type: shell (1) Units: MKS Dimensions: radius: 1thickness: 0.01 Material Properties: Mass Density: 0.007Cost Per Unit Mass: 0Young's Modulus: 210000 Poisson's Ratio: 0.3Thermal Expansion: 0Conductivity: 0
 Constraints Location Degrees of Freedom constraint1 placed on curve A-B:placed on curves A-D and B-C: fixed in all DOFfixed in TransZ, RotX, and RotY
 Loads: Location/Magnitude: Distribution Spatial Variation load1 placed on curve C-D: MZ=0.001 force per unit length uniform
Comparison of Results Data
 Theory Structure1 % Difference Sxx on outer surface at point E 60.0 59.6 .67% Convergence %: 0.9% on Local Disp and SE Max P: 5 No. Equations: 66
1 You cannot view the results information in the summary file. To view the results, you must define a result window for measure Stress XX (Top) with Face Grid on, and query the value at point E.
mvss020: Beam Sections
 Analysis Type: Static Model Type: 3D Comparison: Theory Reference: Roark, R.J., and Young, W.C. Formulas for Stress and Strain. 5th Edition. NY: McGrawHill Book Co. 1982, p. 64. Description: A cantilever beam is subjected to transverse loads in Y and Z and axial load in X . Find the deflection at the free end, the bending stress at the fixed end, and the axial stress along the beam.
This Beam Sections model contains the following element types and corresponding results:
Square Beam
Rectangle Beam
Hollow Rectangle Beam
Channel Beam
I-Section Beam
L-Section Beam
Diamond Beam
Solid Circle Beam
Hollow Circle Beam
Ellipse Beam
Hollow Ellipse Beam
 In all cases, the displacement results are dependent upon the direction of the load. Thus, in this problem, all the results listed as Deflection at Tip may be interpreted as positive or negative.
Square Beam
Specifications
 Element Type: Square Beam Units: IPS Dimensions: a: 0.25 Beam Properties: Area: 0.0625IYY: 0.000325521Shear FY: 10001CY: 0.125 J: 0.000549316IZZ: 0.000325521Shear FZ: 10001CZ: 0.125 Material Properties: Mass Density: 0Cost Per Unit Mass: 0Young's Modulus: 3e7 Poisson's Ratio: 0.3Thermal Expansion: 0Conductivity: 0 Constraints: placed on point A: fixed in all DOF Load: Location: Magnitude: axial placed on point B FX=100 transverse y placed on point B FY=100 transverse z placed on point B FZ=100
1 Structure beams consider shear; however, the represented theoretical problem does not. The values for shear factor compensate for this.
Comparison of Results Data (Square Beam)
 Load Measure Name Theory Structure % Difference Deflection at Tip: axial sq_d_x 1.6e-3 1.6e-3 0% transverse y sq_d_y 9.216e1 9.216e1 0% transverse z sq_d_z 9.216e1 9.216e1 0% Stress: axial sq_s_ten 1.6e3 1.6e3 0% transverse y sq_s_bnd 1.152003e6 1.15200e6 0% transverse z sq_s_bnd 1.152003e6 1.15200e6 0%
 Load Lcl Disp & SE Max P No. Equations Convergence: axial 0% 2 264 transverse y 0% 2 264 transverse z 0% 2 264
Rectangle Beam
Specifications
 Element Type: Rectangle Beam Units: IPS Dimensions: b: 1d: 0.25 Beam Properties: Area: 0.25IYY: 0.0208333Shear FY: 10001CY: 0.125 J: 0.00438829IZZ: 0.00130208Shear FZ: 10001CZ: 0.5 Material Properties: Mass Density: 0Cost Per Unit Mass: 0Young's Modulus: 3e7 Poisson's Ratio: 0.3Thermal Expansion: 0Conductivity: 0 Constraints: placed on point A: fixed in all DOF Load: Location: Magnitude: axial placed on point B FX=100 transverse y placed on point B FY=100 transverse z placed on point B FZ=100
1Structure beams consider shear; however, the represented theoretical problem does not. The values for shear factor compensate for this.
Comparison of Results Data (Rectangle Beam)
 Load Measure Name Theory Structure % Difference Deflection at Tip: axial rct_d_x 4.0e-4 4.0e-4 0% transverse y rct_d_y 2.304e1 2.304e1 0% transverse z rct_d_z 1.44 1.44 0% Stress: Load Measure Name Theory Structure % Difference axial rct_s_ten 4.0e2 4.0e2 0% transverse y rct_s_bnd 2.880e5 2.880e5 0% transverse z rct_s_bnd 7.200e4 7.200e4 0%
 Load Lcl Disp & SE Max P No. Equations Convergence: axial 0% 2 264 transverse y 0% 2 264 transverse z 0% 2 264
Hollow Rectangle Beam
Specifications
 Element Type: Hollow Rectangle Beam Units: IPS Dimensions: b: 1bi: 0.875d: 0.25di: 0.125 Beam Properties: Area: 0.140625IYY: 0.013855Shear FY: 10001CY: 0.125 J: 0.00343323IZZ: 0.00115967Shear FZ: 10001CZ: 0.5 Material Properties: Mass Density: 0Cost Per Unit Mass: 0Young's Modulus: 3e7 Poisson's Ratio: 0.3Thermal Expansion: 0Conductivity: 0 Constraints: placed on point A: fixed in all DOF Load: Location: Magnitude: axial placed on point B FX=100 transverse y placed on point B FY=100 transverse z placed on point B FZ=100
1 Structure beams consider shear; however, the represented theoretical problem does not. The values for shear factor compensate for this.
Comparison of Results Data (Hollow Rectangle Beam)
 Load Measure Name Theory Structure % Difference Deflection at Tip: axial hrct_d_x 7.112e-4 7.111e-4 0.02% transverse y hrct_d_y 2.5869e1 2.5876e1 0.027% transverse z hrct_d_z 2.1653 2.1677 0.10% Stress: Load Measure Name Theory Structure % Difference axial hrct_s_ten 7.112e2 7.111e2 0.01% transverse y hrct_s_bnd 3.2337e5 3.2336e5 0.003% transverse z hrct_s_bnd 1.0826e5 1.0826e5 0%
 Load Lcl Disp & SE Max P No. Equations Convergence: axial 0% 2 264 transverse y 0% 2 264 transverse z 0% 2 264
Channel Beam
Specifications
 Element Type: Channel Beam Units: IPS Dimensions: b: 1di: 1t: 0.125tw: 0.125 Beam Properties: Area: 0.375IYY: 0.0369466Shear FY: 10001CY: 0.625 J: 0.00179932IZZ: 0.0898438Shear FZ: 10001CZ: 0.645833 Material Properties: Mass Density: 0Cost Per Unit Mass: 0Young's Modulus: 3e7 Poisson's Ratio: 0.3Thermal Expansion: 0Conductivity: 0 Constraints: placed on point A: fixed in all DOF Load: Location: Magnitude: axial placed on point B FX=100 transverse y placed on point B FY=100 transverse z placed on point B FZ=100
1 Structure beams consider shear; however, the represented theoretical problem does not. The values for shear factor compensate for this.
Comparison of Results Data (Channel Beam)
 Load Measure Name Theory Structure % Difference Deflection at Tip: axial chnl_d_x 2.6667e-4 6.061674e-04 0% transverse y chnl_d_y 3.339e-1 -3.339e-1 0% transverse z chnl_d_z 8.1198e-1 -8.1198e-1 0% Stress: Load Measure Name Theory Structure % Difference axial chnl_s_ten 2.6667e2 2.6667e2 0% transverse y chnl_s_bnd 2.087e4 2.087e4 0% transverse z chnl_s_bnd 5.244e4 5.244e4 0%
 Convergence: Load Lcl Disp & SE Max P No. Equations axial 0% 4 264 transverse y 0% 4 264 transverse z 0% 4 264
I-Section Beam
Specifications
 Element Type: I-Section Beam Units: IPS Dimensions: b: 1di: 1t: 0.125tw: 0.125 Beam Properties: Area: 0.375IYY: 0.0209961Shear FY: 10001CY: 0.625 J: 0.00179932IZZ: 0.0898438Shear FZ: 10001CZ: 0.5 Material Properties: Mass Density: 0Cost Per Unit Mass: 0Young's Modulus: 3e7 Poisson's Ratio: 0.3Thermal Expansion: 0Conductivity: 0 Constraints: placed on point A: fixed in all DOF Load: Location: Magnitude: axial placed on point B FX=100 transverse y placed on point B FY=100 transverse z placed on point B FZ=100
1 Structure beams consider shear; however, the represented theoretical problem does not. The values for shear factor compensate for this.
Comparison of Results Data (I-Section Beam)
 Load Measure Name Theory Structure % Difference Deflection at Tip: axial I_d_x 2.6667e-4 2.6667e-4 0% transverse y I_d_y 3.3391e-1 3.3573e-1 0.54% transverse z I_d_z 1.4288 1.4296 0.05% Stress: Load Measure Name Theory Structure % Difference axial I_s_ten 2.6667e2 2.6667e2 0% transverse y I_s_bnd 2.0870e4 2.0869e4 0.004% transverse z I_s_bnd 7.1442e4 7.14418e4 0.001%
 Load Lcl Disp & SE Max P No. Equations Convergence: axial 0% 2 264 transverse y 0% 2 264 transverse z 0% 2 264
L-Section Beam
Specifications
 Element Type: L-Section Beam Units: IPS Dimensions: b: 1d: 1t: 0.125tw: 0.125 Beam Properties: Area: 0.25IYY: 0.0105794Shear FY: 10001CY: 0.789352 J: 0.00119955IZZ: 0.0423177Shear FZ: 10001CZ: 0.433047 Material Properties: Mass Density: 0Cost Per Unit Mass: 0Young's Modulus: 3e7 Poisson's Ratio: 0.3Thermal Expansion: 0Conductivity: 0 Constraints: placed on point A: fixed in all DOF Load: Location: Magnitude: axial placed on point B FX=100 transverse y placed on point B FY=100 transverse z placed on point B FZ=100
1 Structure beams consider shear; however, the represented theoretical problem does not. The values for shear factor compensate for this.
Comparison of Results Data (L-Section Beam)
 Load Measure Name Theory Structure % Difference Deflection at Tip: axial L_d_x 4.0e-4 4.0e-4 0% transverse y L_d_y 7.0892e-1 7.1017e-1 0.17% transverse z L_d_z 2.8357 2.8369 0.04% Stress: Load Measure Name Theory Structure % Difference axial L_s_ten 4e2 4e2 0% transverse y L_s_ben 5.5611e4 0 — transverse z L_s_ben 1.228e5 0 —
 Load Lcl Disp & SE Max P No. Equations Convergence: axial 0% 2 264 transverse y 0% 2 264 transverse z 0% 2 264
Diamond Beam
Specifications
 Element Type: Diamond Beam Units: IPS Dimensions: b: 0.25d: 0.25 Beam Properties: Area: 0.03125IYY: 8.13802e5Shear FY: 10001CY: 0.125 J: 0.000146484IZZ: 8.13802e5Shear FZ: 10001CZ: 0.125 Material Properties: Mass Density: 0Cost Per Unit Mass: 0Young's Modulus: 3e7 Poisson's Ratio: 0.3Thermal Expansion: 0Conductivity: 0 Constraints: placed on point A: fixed in all DOF Load: Location: Magnitude: axial placed on point B FX=100 transverse y placed on point B FY=100 transverse z placed on point B FZ=100
1 Structure beams consider shear; however, the represented theoretical problem does not. The values for shear factor compensate for this.
Comparison of Results Data (Diamond Beam)
 Load Measure Name Theory Structure % Difference Deflection at Tip: axial dmnd_d_x 3.2e-3 3.2e-3 0% transverse y dmnd_d_y 3.6864e2 3.6864e2 0% transverse z dmnd_d_z 3.6864e2 3.6864e2 0% Stress: Load Measure Name Theory Structure % Difference axial dmnd_s_ten 3.2e3 3.2e3 0% transverse y dmnd_s_bnd 4.608e6 4.608e6 0% transverse z dmnd_s_bnd 4.608e6 4.608e6 0%
 Load Lcl Disp & SE Max P No. Equations Convergence: axial 0% 2 264 transverse y 0% 2 264 transverse z 0% 2 264
Solid Circle Beam
Specifications
 Element Type: Solid Circle Beam Units: IPS Dimensions: r: 0.25 Beam Properties: Area: 0.19635IYY: 0.00306796Shear FY: 10001CY: 0.25 J: 0.00613592IZZ: 0.00306796Shear FZ: 10001CZ: 0.25 Material Properties: Mass Density: 0Cost Per Unit Mass: 0Young's Modulus: 3e7 Poisson's Ratio: 0.3Thermal Expansion: 0Conductivity: 0 Constraints: placed on point A: fixed in all DOF Load: Location: Magnitude: axial placed on point B FX=100 transverse y placed on point B FY=100 transverse z placed on point B FZ=100
1 Structure beams consider shear; however, the represented theoretical problem does not. The values for shear factor compensate for this.
Comparison of Results Data (Solid Circle Beam)
 Load Measure Name Theory Structure % Difference Deflection at Tip: axial crcl_d_x 5.093e-4 5.092e-4 0.019% transverse y crcl_d_y 9.77848 9.77995 0.015% transverse z crcl_d_z 9.77848 9.77995 0.015% Stress: axial crcl_s_ten 5.093e2 5.092e2 0.019% transverse y crcl_s_bnd 2.44462e5 2.44462e5 0% transverse z crcl_s_bnd 2.44462e5 2.44462e5 0%
 Load Lcl Disp & SE Max P No. Equations Convergence: axial 0% 2 264 transverse y 0% 2 264 transverse z 0% 2 264
Hollow Circle Beam
Specifications
 Element Type: Hollow Circle Beam Units: IPS Dimensions: ri: 0.25 Beam Properties: Area: 0.147262IYY: 0.00287621Shear FY: 100001CY: 0.25 J: 0.00575243IZZ: 0.00287621Shear FZ: 10001CZ: 0.25 Material Properties: Mass Density: 0Cost Per Unit Mass: 0Young's Modulus: 3e7 Poisson's Ratio: 0.3Thermal Expansion: 0Conductivity: 0 Constraints: placed on point A: fixed in all DOF Load: Location: Magnitude: axial placed on point B FX=100 transverse y placed on point B FY=100 transverse z placed on point B FZ=100
1 Structure beams consider shear; however, the represented theoretical problem does not. The values for shear factor compensate for this.
Comparison of Results Data (Hollow Circle Beam)
 Load Measure Name Theory Structure % Difference Deflection at Tip: axial hcr_d_x 6.7906e-4 6.7906e-4 0% transverse y hcr_d_y 1.04304e1 1.04331e1 0.025% transverse z hcr_d_z 1.04304e1 1.04332e1 0.026% Stress: axial hcr_s_ten 6.7906e2 6.7906e2 0% transverse y hcr_s_bnd 2.6076e5 2.6075e5 0.003% transverse z hcr_s_bnd 2.6076e5 2.6076e5 —
 Load Lcl Disp & SE Max P No. Equations Convergence: axial 0% 2 264 transverse y 0% 2 264 transverse z 0% 2 264
Ellipse Beam
Specifications
 Element Type: Ellipse Beam Units: IPS Dimensions: a: 1b: 0.25 Beam Properties: Area: 0.785398IYY: 0.19635Shear FY: 10001CY: 0.25 J: 0.0461999IZZ: 0.0122718Shear FZ: 10001CZ: 1 Material Properties: Mass Density: 0Cost Per Unit Mass: 0Young's Modulus: 3e7 Poisson's Ratio: 0.3Thermal Expansion: 0Conductivity: 0 Constraints: placed on point A: fixed in all DOF Load: Location: Magnitude: axial placed on point B FX=100 transverse y placed on point B FY=100 transverse z placed on point B FZ=100
1 Structure beams consider shear; however, the represented theoretical problem does not. The values for shear factor compensate for this.
Comparison of Results Data (Ellipse Beam)
 Load Measure Name Theory Structure % Difference Deflection at Tip: axial elps_d_x 1.2732e-4 1.2732e-4 0% transverse y elps_d_y 2.4446 2.4445 0.004% transverse z elps_d_z 1.527887e-1 1.531516e-1 0.23% Stress: axial elps_s_ten 1.273239e2 1.27324e2 0% transverse y elps_s_bnd 6.11155e4 6.111550e4 0% transverse z elps_s_bnd 1.527887e4 1.527887e+04 0%
 Load Lcl Disp & SE Max P No. Equations Convergence: axial 0% 2 264 transverse y 0% 2 264 transverse z 0% 2 264
Hollow Ellipse Beam
Specifications
 Element Type: Hollow Ellipse Beam Units: IPS Dimensions: a: 1b: 0.25ai: 0.875 Beam Properties: Area: 0.184078IYY: 0.081253Shear FY: 10001CY: 0.25 J: 0.0191184IZZ: 0.00507832Shear FZ: 10001CZ: 1 Material Properties: Mass Density: 0Cost Per Unit Mass: 0Young's Modulus: 3e7 Poisson's Ratio: 0.3Thermal Expansion: 0Conductivity: 0 Constraints: placed on point A: fixed in all DOF Load: Location: Magnitude: axial placed on point B FX=100 transverse y placed on point B FY=100 transverse z placed on point B FZ=100
1 Structure beams consider shear; however, the represented theoretical problem does not. The values for shear factor compensate for this.
Comparison of Results Data (Hollow Ellipse Beam)
 Load Measure Name Theory Structure % Difference Deflection at Tip: axial hel_d_x 5.4325e-4 5.4324e-4 0.0018% transverse y hel_d_y 5.9075 5.9091 0.45% transverse z hel_d_z 3.6922e-1 3.7091e-1 0.027% Stress: axial hel_s_ten 5.4325e2 5.4324e2 0.0018% transverse y hel_s_bnd 1.4769e5 1.4768e5 0.0027% transverse z hel_s_bnd 3.6922e4 3.6921e4 0.0067%
 Load Lcl Disp & SE Max P No. Equations Convergence: axial 0% 2 264 transverse y 0% 2 264 transverse z 0% 2 264
mvss021:Thick-Walled Cylinder Under Internal Pressure
 Analysis Type: Static Model Type: 3D Reference: Roark, R.J., and Young, W.C. Formulas for Stress and Strain. NY: McGraw-Hill Book Co., 5th edition, Table 32, Case 1. Description: A thick-walled cylinder subjected to an internal pressure is free to expand in all directions. Obtain maximum radial and circumferential stresses.
Specifications
 Element Type: tets (133) Units: IPS Dimensions: length: 20Ro: 6Ri: 4 Material Properties: Mass Density: 0.0002614Cost Per Unit Mass: 0Young's Modulus: 1.06e7 Poisson's Ratio: 0.33Thermal Expansion: 1.25e05Conductivity: 9.254
 Constraints Location Degrees of Freedom constraint1 placed on point A:placed on point B:placed on point D: fixed in TransX, TransY, and TransZfixed in TransYfixed in TransY and TransZ
 Loads: Location/Magnitude: Distribution Spatial Variation pressure placed on all internal surfaces: pressure = 1000 total load/unit area uniform
Comparison of Results Data
 Theory Structure % Difference yy along edges C-E & F-G 2600 2603.7325 0.14% xx along edges C-E & F-G 1000 999.1724 0.08% Multi-Pass Convergence %: The analysis converged to within 1% on measures. Max P: 6 No. Equations: 1875
mvss022: Thin-Walled Spherical Vessel Under Its Own Weight
 Analysis Type: Static Model Type: 3D Cyclic Symmetric Reference: Roark, R.J., and Young, W.C. Formulas for Stress and Strain. NY: McGraw-Hill Book Co., 5th edition, Table 29, Case 3c. Description: A thin-walled half-spherical vessel is subjected to its own weight (gravity load). Obtain the hoop stress at points A and B.
Specifications
 Element Type: shells (3) Units: IPS Dimensions: R: 10 Material Properties: Mass Density: 0.0002588Cost Per Unit Mass: 0Young's Modulus: 1.0e7 Poisson's Ratio: 0.3Thermal Expansion: 0Conductivity: 0
 Constraints Location Degrees of Freedom constraint1 Edges @ = 0 & = 90:Edge @ z = 0:Placed on point C @ r = 10, = 0, z = 0: cyclical symmetryfixed in TransZfixed in TransR, TransT, and TransZ
 Load: Direction: Magnitude: gravity xyz 0.0386.40.0
Comparison of Results Data
 Theory Structure % Difference zz at point A: 1 0.987 1.3% tt at point B: -1 -0.982 1.8% Multi-Pass Adaptive Convergence %: The analysis converged to within 4.9% on Local Displacement and Element Strain Energy. It converged to 1.7% on Global RMS Stress. Max P: 9 No. Equations: 773
mvsl001: Static Analysis of Composite Lay-up
 Analysis Type: Static with Orthotropic Material Properties Model Type: 3D Comparison: Theory Reference: Noor, A.K. and Mathers, M.D., "Shear-Flexible Finite-Element Models of Laminated Composite Plates and Shells." NASA TN D-8044; Langley Research Center, Hampton, Va. Dec. 1975. Description: Determine maximum resultant bending moment and transverse deformation in a clamped, nine-layered, orthotropic square plate.
Specifications
 Element Type: shell (4) Units: IPS Dimensions: length: 2.5width: 2.5thickness: 0.5 Shell Properties: Extensional Stiffness A11=10.266 A12=0.1252 A16=0 A22=10.266 A26=0 A66=0.3 ExtensionalBending Coupling Stiffness B11=0 B12=0 B16=0 B22=0 B26=0 B66=0 Bending Stiffness D11=0.25965 D12=0.0026082 D16=0 D22=0.1681 D26=0 D66=0.00625 Transverse Shear Stiffnesses A55=0.275004 A45=0 A44=0.275004 Mass per Unit Area 7.2915e5 Rotary Inertia per Unit Area 1.5191e5 Thermal Resultant Coefficients: Force N11=0 N22=0 N12=0 Moment M11=0 M22=0 M12=0 Stress Recovery Locations CZ Ply Orientation (Degrees) Material Location Reported for "Top" in Results 0.25 0 trniso1 Location Reported for "Bottom" in Results 0.25 0 trniso1 Material Properties: Mass Density: 0.00014583 Cost Per Unit Mass: 0 Young's Moduli E1=4e1 E2=1 E3=1 Poisson's Ratio Nu21=0.25 Nu31=0.25 Nu32=0 Shear Moduli G21=0.6 G31=0.6 G32= E2/[2*(1+Nu32)] Coefficients of Thermal Expansion a1=0 a2=0 a3=0 Constraints: symmetry constraints on edges B-C and C-Dclamped on edges A-B and A-D Loads: uniform pressure load over the entire surface = 1
Comparison of Results Data
 Theory Structure % Difference Displacement 11.596 11.84151 2.11% Bending Moment 1 1.4094 1.41307 0.26% Convergence %: 1.1% on local displacement and element strain energy and 2.2 % on global RMS stress. Max P: 3 No. Equations: 76
1 To verify this Creo Simulate result, create a query result window for the quantity Moment:Shell Resultant:XX. Show the result window and query for the value in the upper left corner of the model. This is obtained using View:Model Min. The absolute value of this negative number is greater than the value reported using View:Model Max and is reported here.