Design sensitivity analysis of critical load factor for nonlinear structural systems

Design sensitivity analysis and topology optimization of displacement–loaded non-linear structures

Improved semi-analytic sensitivity analysis combined with a higher order approximation scheme in the framework of adjoint variable method

A continuum-based sizing design sensitivity analysis (DSA) method is presented for the transient dynamic response of non-linear structural systems with elastic–plastic material and large deformation. The methodology is aimed for applications in non-linear dynamic problems, such as crashworthiness design. The first-order variations of the energy forms, load form, and kinematic and structural responses with respect to sizing design variables are derived. To obtain design sensitivities, the direct differentiation method and updated Lagrangian formulation are used since they are more appropriate for the path-dependent problems than the adjoint variable method and the total Lagrangian formulation, respectively. The central difference method and the finite element method are used to discretize the temporal and spatial domains, respectively. The Hughes–Liu truss/beam element, Jaumann rate of Cauchy stress, rate of deformation tensor, and Jaumann rate-based incrementally objective stress integration scheme are used to handle the finite strain and rotation. An elastic–plastic material model with combined isotropic/kinematic hardening rule is employed. A key development is to use the radial return algorithm along with the secant iteration method to enforce the consistency condition that prevents the discontinuity of stress sensitivities at the yield point. Numerical results of sizing DSA using DYNA3D yield very good agreement with the finite difference results. Design optimization is carried out using the design sensitivity information. Copyright © 2000 John Wiley & Sons, Ltd.

Critical load, dynamic characteristics and parametric instability of electrorheological material-based adaptive beams

Using the bond-based peridynamics and the parallel computation with binary decomposition, an adjoint shape design sensitivity analysis(DSA) method is developed for the dynamic crack propagation problems. The peridynamics includes the successive branching of cracks and employs the explicit scheme of time integration. The adjoint variable method is generally not suitable for path-dependent problems but employed since the path of response analysis is readily available. The accuracy of analytical design sensitivity is verified by comparing it with the finite difference one. The finite difference method is susceptible to the amount of design perturbations and could result in inaccurate design sensitivity for highly nonlinear peridynamics problems with respect to the design. It turns out that C1-continuous volume fraction is necessary for the accurate evaluation of shape design sensitivity in peridynamic discretization.

Effects of material nonlinearity on the global analysis and stability of stainless steel frames

Load carrying capacity of systems within a global safety perspective. Part I. Robustness of stable equilibria under imperfections

This paper presents an investigation of the dynamic buckling phenomenon in thin-walled Fiber Metal Laminate short columns subjected to axial compressive loading. The numerical analysis is performed with the FEM ANSYS software for three profiles differentiate in the laminate stacking sequence. Two groups of criteria were implemented to assess the structure resistance to dynamic pulse loading: the dynamic buckling criteria and strength failure criteria. Parametric analysis was performed to determine the effect of initial geometric imperfection, laminate stacking sequence, and the pulse load's shape on the dynamic stability. The value of the amplitude of initial geometric imperfection and the shape of pulse load influence the value of critical Dynamic Load Factor strongly. Aluminium yielding was observed as the primary failure source developed in the FML structure subjected to the pulse loading.

Microstructure design of porous viscoelastic composites with prescribed relaxation moduli by multi-material topology optimization

The structure and the characteristics of an optimal design procedure of electromagnetic devices are examined and the three different approaches to design sensitivity derivation are reviewed. For the shape design problems of the transient eddy current systems driven by voltage sources, the design sensitivity is derived in an explicit form to the design variables using the finite element algebraic system equation and the adjoint variable method. The original state variable equation is an initial value problem, but the adjoint variable equation is derived as a terminal value problem. Both equations are solved using a time-stepping finite element method. As a numerical example, the coil-positioning problem of an induction heating system is tested and the proposed algorithm is validated.

Adjoint design sensitivity analysis and optimization of nonlinear structures using geometrical mapping approach

A topology optimization method in rarefied gas flow problems using the Boltzmann equation

Dielectric breakdown model for a conductive crack and electrode in piezoelectric materials

Reliability-based design optimization and uncertainty quantification for optimal conditions of composite structures with non-linear behavior

Minimum-weight design of structural frames