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>Design sensitivity analysis and optimization of transient dynamic response of nonlinear structures with elastic-plastic material and large deformation.
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Design sensitivity analysis and optimization of transient dynamic response of nonlinear structures with elastic-plastic material and large deformation.
A continuum-based design sensitivity analysis (DSA) method is developed for the transient dynamic response of nonlinear structural systems with rate-independent elastic-plastic material under large strain and large rotation assumptions using the established nonlinear finite element code DYNA3D.; The explicit central difference method and the finite element method are incorporated for time and physical domain discretizations, using the updated Lagrangian formulation, respectively. An elastic-plastic material model, with rate-independent plasticity, that involves the isotropic/kinematic hardening effect is incorporated. The radial return method, along with the secant iteration method under plane plasticity assumption is used to enforce the consistency condition. Hughes-Liu truss/beam element formulation is used to account for the large strain effect. The Jaumann rate of Cauchy stress, the rate of deformation tensor, and the Jaumann rate based incrementally objective stress integration scheme are employed to handle the large rotation effect.; The first-order variations of the kinetic energy form, the strain energy form, the load form, and kinematic/structural responses with respect to sizing and configuration design variables are derived. For the configuration design, both shape and orientation variations will cause the first-order variations of the equations of motion. The direct differentiation method is used since the adjoint variable method is not appropriate for the DSA of the path dependent problems. Each adjoint solution yields the sensitivity of only one performance measure at a fixed time, rather than the sensitivities of the full transient response fields.; Since the updated Lagrangian formulation is used, the design velocity field which describes the mapping relationship from the original design to the perturbed design, should be updated. This updated design velocity field is used to predict the solution at the next configuration of the perturbed design.; A numerical example demonstrates that erroneous DSA results may accumulate when the design sensitivity of the variable time step is used. Numerical implementations of sizing and configuration DSA of truss and beam structures with impact loads are carried out for several engineering problems. Finally, the design sensitivity information is used for the iterative sizing and configuration design optimization of the vehicle frame and the A-pillar models.
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