Analysis and Improvement of Virtual Work Criteria for Structure Optimization
An improvement of virtual work criteria for structure optimization is presented to overcome the shortcomings caused by the neglect of dead weight and inertial load of structure in solution of criteria equations. Deduction of criteria equations is analyzed to prove that the shortcomings lead to the error of structure optimization. Therefore, new criteria equations are formulated using the displacement representation of algebraic sum and matrices. According to the characteristics of the improved criteria equations, an improved Aitken algorithm is applied to solve the equations in order to implement the complete automatization of iterative solution for structure optimization. The algorithm is proved to be an accelerated iterative method, and its convergence order is estimated. The feasibility of improved criteria equations and the merits of improved Aitken algorithm are demonstrated by an illustrative example showing five-bar truss. The results show that the improvement of virtual work criteria provides a structure optimization method for precision machine.
An algorithm for grouping members in a structure
Abstract An automated method for grouping discrete structural members is presented in this paper. The number of groups is specified by the user, and members are grouped according to their mass per unit length. The method first optimizes a structure assuming that every member can have a different section. This is done using the Virtual Work Optimization (VWO) method, but any method can be used. The initial solution is the lightest possible, but the number of sections required makes it impractical and uneconomical to construct. Next, an exhaustive search of all possible grouping permutations is carried out. The mass of the structure is predicted for each permutation. The permutation which results in the lightest structure is selected. The structure is passed through the optimization process one last time. The solution produced satisfies all strength and deflection criteria. A method for reducing computational cost is proposed to address very large structures. Four case studies are presented to demonstrate the effectiveness of the grouping algorithm. A stepped cantilever, a 15 storey frame, a truss and a warehouse are investigated. As an example of results, the 195 members of the 15 storey frame are placed into 25 groups to produce a structure only 2.4% heavier than the ungrouped solution. The configuration computed is 5.9% lighter than grouping the structure using the method found in the literature.
Optimization of 3d trusses with adaptive approach in genetic algorithms
This paper discusses the adaptive approach in genetic algorithms (GAs). It is tried to show how the adaptive approach affects the performance of GAs, suggesting some improvements in both the penalty function, and mutation and crossover. A strategy is also considered for member grouping to reduce the size of the problem. Some practical design of space truss examples taken from technical literature are optimized by the algorithm suggested in the current work. Design constraints such as displacement, tensile stress and stability given by national specifications are incorporated and the results are compared with the ones obtained by previous studies. It is concluded that the member grouping together with the adaptive approach increase the probability of catching the global solution and enhance the performance of GAs.