Design sensitivity analysis of non‐linear structural systems part I: Theory

TLDR

The paper proposes a unified framework for design sensitivity analysis of nonlinear structural systems, enabling the optimization of sizing design variables. The method treats geometric and material nonlinearities, retains continuum elasticity in a distributed‑parameter framework, and derives adjoint‑based sensitivity expressions that can be evaluated numerically with finite element analysis.

Abstract

Abstract A unified approach is presented for design sensitivity analysis of non‐linear structural systems that include truss, beam, plane elastic solid and plate components. Both geometric and material non‐linearities are treated. Sizing design variables, such as thickness and cross‐sectional areas of components of individual members and built‐up structures, are considered. A distributed parameter structural design sensitivity analysis approach is used that retains the continuum elasticity formulation throughout the derivation of design sensitivity analysis results. Using this approach and an adjoint variable method, expressions for design sensitivity in terms of design variations are derived in the continuous setting which can be evaluated numerically using analysis results of finite element analysis. Both total Lagrangian and updated Lagrangian formulations in non‐linear analysis of solid mechanics are used for design sensitivity analysis. Numerical implementation of design sensitivity analysis results using existing finite element code will be presented in Part II of this paper.