A series of hybrid strain-based three-node flat triangular shell elements is developed for struct... more A series of hybrid strain-based three-node flat triangular shell elements is developed for structural analyses. For linear analyses, the Hellinger Reissner (H-R) variational principle is employed. The elements are obtained by combining a triangular bending element and a plane stress element. For nonlinear analysis, the updated Lagrangian formulation and the incremental H-R variational principle are applied. The incremental second Piola Kirchhoff stress and the incremental Washizu strain are chosen as incremental stress and strain measures. Material nonlinearity is of the elastoplastic type with isotropic hardening. In all cases, explicit expressions for the stiffness and consistent mass matrices are obtained. The various shell structures studied show that the element formulations are accurate, effective, flexible, and applicable to thin to moderately thick shells with geometrical and material nonlinearities. In parallel, the stochastic central difference (SCD) method is applied to determine response statistics of general structures. The SCD method is extended to include a relatively general nonstationary random excitation comprising deterministic and stochastic components. It is applied to compute the random responses of general nonlinear shell structures. Numerical results employing the proposed methodologies are presented and their effectiveness is addressed.
A series of hybrid strain-based three-node flat triangular shell elements is developed for struct... more A series of hybrid strain-based three-node flat triangular shell elements is developed for structural analyses. For linear analyses, the Hellinger Reissner (H-R) variational principle is employed. The elements are obtained by combining a triangular bending element and a plane stress element. For nonlinear analysis, the updated Lagrangian formulation and the incremental H-R variational principle are applied. The incremental second Piola Kirchhoff stress and the incremental Washizu strain are chosen as incremental stress and strain measures. Material nonlinearity is of the elastoplastic type with isotropic hardening. In all cases, explicit expressions for the stiffness and consistent mass matrices are obtained. The various shell structures studied show that the element formulations are accurate, effective, flexible, and applicable to thin to moderately thick shells with geometrical and material nonlinearities. In parallel, the stochastic central difference (SCD) method is applied to determine response statistics of general structures. The SCD method is extended to include a relatively general nonstationary random excitation comprising deterministic and stochastic components. It is applied to compute the random responses of general nonlinear shell structures. Numerical results employing the proposed methodologies are presented and their effectiveness is addressed.
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