E.5 Material Nonlinear Solid and Shell Element

Nonlinear behavior tests were conducted for continuum and shell elements using various material models, including von Mises, Tresca, Drucker–Prager, and Mohr–Coulomb, applied to cantilever and simply supported beam models.

• Cantilever model: 2000 × 400 × 100 mm

• Simply supported beam model: 4000 × 400 × 100 mm

• Material model (perfectly plastic, \(E = 200\ \text{GPa}\), \(f_{y} = 400\ \text{MPa}\))

  • von Mises, Tresca, Drucker–Prager, Mohr–Coulomb

• Default mesh size

  • C3D8 elements: 20 × 4 × 1 (cantilever), 40 × 4 × 1 (simply supported beam)
  • CPS4 elements: 20 × 4 (cantilever), 40 × 4 (simply supported beam)
  • CS8 elements: 20 × 1 (cantilever), 40 × 1 (simply supported beam)
  • S4 elements: 20 × 1 (cantilever), 40 × 1 (simply supported beam)

• Shell elements (S4, CS8) : vertical integration: Legendre, 9 points

Overall, the analysis results show good agreement with the analytical solutions. However, differences may occur near the fixed end due to the constraint effects in the \(y\) and \(z\) directions. In particular, when applying the von Mises and Drucker–Prager models, larger discrepancies are observed in nonlinear behavior due to the effects of transverse thickness strain.

Figure E.5.1 Cantilever Models (C3D8, CPS4, CS8, S4 element)

Figure E.5.2 Simply Support Beam Models (C3D8, CPS4, CS8, S4 element)

Figure E.5.3 Analysis Results of Cantilever

Figure E.5.4 Analysis Results of Simply Supported Beam

Input File

• cant-c3d8.inp : Cantilever, C3D8

• cant-cps4.inp : Cantilever, CPS4

• cant-cs8.inp : Cantilever, CS8

• cant-s4.inp : Cantilever, S4

• beam-c3d8.inp : Simply Supported Beam, C3D8

• beam-cps4.inp : Simply Supported Beam, CPS4

• beam-cs8.inp : Simply Supported Beam, CS8

• beam-s4.inp : Simply Supported Beam, S4