An improved gradient-based method to solve parametric optimisation problems of the bar structures

Abstract

The paper considers parametric optimisation problems for the bar structures formulated as nonlinear programming tasks. The method of the objective function gradient projection onto the active constraints surface with simultaneous correction of the constraints violations has been used to solve the parametric optimisation problem. Equivalent Householder transformations of the resolving equations of the method have been proposed. They increase numerical efficiency of the algorithm developed based on the method under consideration. Additionally, proposed improvement for the gradient-based method also consists of equivalent Givens transformations of the resolving equations. They ensure acceleration of the iterative searching process in the specified cases described by the paper due to decreasing the amount of calculations. The comparison of the optimisation results of truss structures presented by the paper confirms the validity of the optimum solutions obtained using proposed improvement of the gradient-based method. The efficiency of the propoced improvement of the gradient-based method has been also confirmed taking into account the number of iterations and absolute value of the maximum violation in the constraints.

Optimal numbers of the redundant members for introducing initial pre-stressing forces into steel bar structures

“…The parametric optimization problem stated as non-linear programming task by (1.1) -(1.3) can be successfully solved using a gradient projection non-linear methods [21] in cases if the purpose function and constraints of the mathematical model are continuously differentiable functions, as well as the search space is smooth [22,23]. The method of objective function gradient projection onto the active constraints surface with simultaneous correction of the constraints violations ensures effective searching for solution of the nonlinear programming tasks occurred when optimum designing of the building structures [24,25]. Additionally, a sensitivity analysis is a useful optional feature [26] that could be used in the scope of numerical algorithms which are developed based on the gradient methods.…”

“…3.1. Design scheme of the cross beam structure with node and bar numbersThe cross-beam structure is subjected to the distributed dead and live loads with characteristic value25.44 q  t/m. Applied loadings on the considered cross-beam structure are transmitted using mezzanine beams arranged with step 1m.For considered cross-beam structure, steel with the following material properties is used: design resistance 240 y R  MPa, modulus of elasticity…”