Total potential energy minimization method in structural analysis considering material nonlinearity

Minimum potential energy principle is the basis of the most of the well-known traditional techniques used in the structural analysis. This principle determines the equilibrium conditions of systems with reference to minimization of the sum of the total potential energy of the structure. In traditional applications, this methodology is formulized by using matrix operations. A methodology has been proposed in the last decades for structural analyses based on the idea of using metaheuristic algorithms to obtain minimum potential energy of the structural system instead of following this classical approach. This new method, called “Total Potential Optimization using Metaheuristic Algorithms (TPO/MA)”, has been applied in this paper to truss structures considering linear and nonlinear behavior of the structural material. The metaheuristic method used in this process is teaching-learning based optimization (TLBO) algorithm. The proposed technique is applied on numerical examples and results are compared with other techniques in order to test the efficiency of the proposed method. According to results obtained, TPO/MA method with TLBO algorithm is a feasible technique for the investigated problem

Elastik Konsol Kirişlerin Büyük Deformasyon Analizi

Konferans Bildirisi -- Teorik ve Uygulamalı Mekanik Türk Milli Komitesi, 2015Conference Paper -- Theoretical and Applied Mechanical Turkish National Committee, 2015Bu çalışma kapsamında elastik konsol bir kirişin statik analizi Euler-Bernoulli eşitlikleri kullanılarak yinelemeli bir yöntemle yapılmıştır. Bu amaçla kiriş eşit uzunlukta parçalara bölünmüş ve ötelenmelerin hesabında, bu parçalar üzerindeki dönmelerin doğrusal değiştiği kabulü yapılmıştır. Başlangıçta kirişe verilen yükün kirişte oluşturduğu şekil değiştirmeler belirlenmiş, şekil değiştirmiş kirişe tekrar aynı yükler etki ettirilerek şekil değiştirmeler doğrusal olmayan şekilde tekrar belirlenmiştir. Bu işlem şekil değiştirme sonuçları yeteri kadar birbirine yaklaştığında bitirilerek kirişin gerçek şekil değiştirmesi bulunmuştur. Yineleme işlemi Ms Excel programlarında yapılmıştır.In the context of this study, structural analysis of an elastic cantilever has been conducted using an iterative method based on Euler-Bernouilli equations. For this purpose, the beam has been considered to be divided into elements of equal length and the rotational angles have been assumed to be linearly changing over these elements in computing the elastic curve. At the beginning, the deformations caused by the loads acting on the structure is determined, and then by application of the loads on the deformed system, the new deflections are re-calculated. This procedure is repeated until stabilization of deflections and rotations. The iterative process has been conducted using MS Excel

Analysis of cable structures through energy minimization

In structural mechanics, traditional analyses methods usually employ matrix operations for obtaining displacement and internal forces of the structure under the external effects, such as distributed loads, earthquake or wind excitations, and temperature changing inter alia. These matrices are derived from the well-known principle of mechanics called minimum potential energy. According to this principle, a system can be in the equilibrium state only in case when the total potential energy of system is minimum. A close examination of the expression of the well-known equilibrium condition for linear problems, P=K Delta, where P is the load vector, K is the stiffness matrix and A is the displacement vector, it is seen that, basically this principle searches the displacement set (or deformed shape) for a system that minimizes the total potential energy of it. Instead of using mathematical operations used in the conventional methods, with a different formulation, meta-heuristic algorithms can also be used for solving this minimization problem by defining total potential energy as objective function and displacements as design variables. Based on this idea the technique called Total Potential Optimization using Meta-heuristic Algorithms (TPO/MA) is proposed. The method has been successfully applied for linear and non-linear analyses of trusses and truss-like structures, and the results have shown that the approach is much more successful than conventional methods, especially for analyses of nonlinear systems. In this study, the application of TPO/MA, with Harmony Search as the selected meta-heuristic algorithm, to cables net system is presented. The results have shown that the method is robust, powerful and accurate

Computation of Nonunique Solutions for Trusses Undergoing Large Deflections

Determination of nonunique configurations of structures is a problem which cannot be treated readily using classical methods of analysis. In the literature, these kinds of problems are tackled for some simple problems, like trusses with a small number of joints and members, and with specially designed approaches. The recent method of analysis called Total Potential Optimization using Metaheuristic Algorithms (TPO/MA), on the other hand, provides an efficient tool for dealing with these kinds of problems, practically without recourse to any special arrangement. In this analysis, using Harmony Search as the metaheuristic algorithm, large truss structures with linear elastic members are investigated under large deflections as to the existence of more than one solution. The results have shown that for the two examples investigated, a tower truss with 25 members and a dome truss with 24 members, nonunique configurations do exist at quite unexpected levels of loads, and that only one of them can be found with normal applications of the well-known Finite Element method