Size Optimization of Statically Loaded Structures by Two Level Multipoint Constraint Approximation and Interior Point Algorithm

This paper presents a scheme for size optimization of statically loaded truss structures under stress and deformation constraints. The method employs maximum stress values of design parameters as initial design and a two level multipoint approximations for constraint approximation along with interior point algorithm for optimization. Interior point algorithm is imposed, instead of dual method, for added numerical controls to avoiding singularities, complex number generations and relevant complications such as function evaluations during complicated optimization calculations which might occur through computation during line search. Another major induction in the algorithm is linear modification of the design variable matrix in beginning of each optimization cycle until it has only one active constraint. The proposition has shown significant reduction in number of optimization cycles. The paper also includes a benchmark example in support of the presented procedure.