The effect of compatibility conditions on optimal design of flexural structures

Abstract

AbstractIn most structural optimization problems the time‐consuming implicit analysis must be repeated many times during the solution process. To alleviate this difficulty, the implicit analysis equations are often neglected or replaced by explicit approximations.Assuming the force method analysis formulation, optimal solutions of two problems are studied and compared: The equilibrium linear programme (ELP), where only explicit equilibrium conditions are considered in the analysis model The non‐linear programme (NLP), where the implicit compatibility conditions are included to obtain a complete formulation. The effect of geometrical parameters on optimal solutions of both problems is investigated and geometries with particular properties are identified. The main observations that have been made are as follows: Multiple optima of the ELP have been obtained for geometries where transitions in the set of active constraints at the ELP optimum occur. The NLP optimum for such a geometry might be included in the set of ELP optima. Identical optimal solutions of the two problems have been found for geometries where transitions in the set of active constraints at the NLP optimum occur. The explicit ELP can be solved instead of the implicit NLP for the two classes of transition geometries.The relationships between optimal force distributions and objective function values for the two problems are studied and examples where compatibility conditions can be neglected are illustrated.