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Optimization algorithms for physically non‐linear structures

A family of numerical methods and algorithms targeted to the optimization of physically non‐linear structures is proposed. The structures are described using finite element approach, they are supposed to be loaded by single static loading. It is assumed that various types of finite elements are used for the description. Buckling effects are neglected. Sizing design variables with prescribed lower limits are considered. The numerical approach is based on the use of physically non‐linear hyperelastic (PNH) model for the description of active loading process for the physically non‐linear structures. Three optimization sub‐problems for the PNH structures are considered. Variational principles for the structures as well as optimality conditions and particular solutions of the sub‐problems are used for the development of algorithms intended for numerical solution of the sub‐problems. Geometrical interpretation of the algorithms is presented. Monotonicity properties of the algorithms are proved under some assumptions. It is indicated how the algorithms may be used for the general case of optimization of physically non‐linear structure under single loading. Numerical examples are presented. Monotonicity of the algorithms is demonstrated. It is noted that no numerical problems arise when some structural members degenerate during numerical process. Copyright © 2001 John Wiley & Sons, Ltd.