Optimization of elastic‐plastic geometrically non‐linear lightweight structures under stiffness and stability constraints

Abstract

An actual structural design, especially that of lightweight structures, must evaluate strength, stiffness and stability constraints. A designed structure must satisfy optimality criteria. One faces known difficulties when trying to implement several from above mentioned requirements into optimization problem for further successful numerical realisation. A method to formulate the optimization problem, incorporating all above described criterions, mathematical model and algorithm to solve it numerically, taking into account the geometrically non‐linear structural behaviour are presented for truss type structure. In each optimization cycle the member forces obtained in the previous optimization cycle via elastic‐plastic non‐linear analysis procedure are employed to obtain the new optimal design values. During the optimization procedures, the tension members are assumed to be loaded up to the yield limit, compression members are assumed to be stressed up to their critical limits, the nodal displacements are restricted to limited magnitudes in prescribed directions. Design examples are presented to demonstrate the application of the algorithm. First Published Online: 14 Oct 2010

Keywords

• elastic‐plastic structure
• optimization
• stiffness and stability constraints
• geometrical non‐linearity
• tangent stiffness method
• finite element discrete model