Abstract
Total Potential Optimization using Metaheuristic Algorithms (TPO/MA) is an alternative tool for the analysis of structures. It is shown that this emerging method is advantageous in solving nonlinear problems like trusses, tensegrity structures, cable networks, and plane stress systems. In the present study, TPO/MA, which does not need any specific implementation for nonlinearity, is demonstrated to be successfully applied to the analysis of plane strain structures. A numerical investigation is performed using nine different metaheuristic algorithms and an adaptive harmony search in linear analysis of a structural mechanics problem having 8 free nodes defined as design variables in the minimization problem of total potential energy. For nonlinear stress-strain relation cases, two structural mechanics problems, one being a thick-walled pipe and the other being a cantilever retaining wall, are analyzed by employing adaptive harmony search, which was found to be the best one in linear analyses. The nonlinear stress-strain relations considered in these analyses are hypothetical ones due to the lack of any such relationship in the literature. The results have shown that TPO/MA can solve nonlinear plane strain problems that can be encountered as engineering problems in structural mechanics.
Highlights
Finite Element Method (FEM) is a well-known mechanical and structural analysis tool that is used commonly by structural engineers
In FEM applications, firstly matrix equations are prepared for each element, and these equations are combined to yield a general matrix equation of the form Kx = p where K is the square matrix called stiffness matrix, x is the vector of displacements and p is the vector of loads
It is shown that Total Potential Optimization using Metaheuristic Algorithms (TPO/MA) is an efficient method in solving plane strain problems too whether the constitutive equation is linear or not
Summary
Finite Element Method (FEM) is a well-known mechanical and structural analysis tool that is used commonly by structural engineers. In FEM applications, firstly matrix equations are prepared for each element, and these equations are combined to yield a general matrix equation of the form Kx = p where K is the square matrix called stiffness matrix, x is the vector of displacements and p is the vector of loads. This operation can be performed for linear and well-constrained systems. As a negative point to FEM, one can cite the problems that are under-constrained. There are several other problems where FEM becomes very difficult to apply, like the cases where the solution is not unique or where there are unilateral or nonlinear constraints [1,2,3,4,5]
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