In this paper, meshless element free Galerkin method has been used to obtain the numerical solution of transient and steady state heat conduction problems in two-dimensional domains. The unknown function of temperature T(x) has been approximated by moving least square approximant} Th(x). These approximants are constructed by using a weight function, a polynomial basis and a set of non-constant coefficients. Variational method is used to obtain the discrete equations. Essential boundary conditions are imposed by Lagrange multiplier technique. Two new weight functions namely hyperbolic and rational have been proposed. The results have been obtained for a two-dimensional model problem using different EFG weight functions and are compared with those obtained by finite element and analytical methods.
Keywords: meshless method, element free Galerkin method, two-dimensional transient and steady heat conduction.
A numerical method is presented for analyzing the mixed mode interface crack between two dissimilar isotropic materials. A simple and efficient solution procedure is developed based on the finite element method and the compliance approach in conjunction with the fundamental relations in fracture mechanics. The procedure makes it possible to separate the Mode I and Mode II stress intensity factors KI and KII respectively for an interfacial crack in bi-material media under different loading conditions. The strain energy release rate is first computed, then using the compliance method and the known auxiliary solutions, the values for KI and KII are evaluated. The procedure is investigated for different crack extensions. The formulations used for computing the strain energy release rate and the stress intensity factors are presented. The method converges to accurate solutions for small crack extensions. A numerical example is presented to demonstrate the accuracy of the proposed model.
Keywords: bi-material interface crack, strain energy release rate, stress intensity factors, finite element analysis, compliance approach.
Optimization theory has advanced considerably during the last three decades, as illustrated by a vast number of published books, surveys, and papers concerning this subject. However, for optimization of complex systems that may not be modeled exactly by Ludwig von Bertalanffy's general system theory, we may need a new philosophy based on rather non-conventional logics. It is represented bellow.
Keywords: complex systems, multi-objective optimization, fuzzy logic, modal logic, multi-valued logic.
In the paper three computational models for crack growth analysis in quasi-brittle materials in plane stress state are presented. These models have been worked out on the base of different methods of coupling the finite element method and the element free Galerkin method. Effectiveness of the methods of analysis are improved by the algorithm of dynamic domain decomposition into Ω, Ωρ, Ωhρ parts. The usefulness of the methods in crack growth analysis has been confirmed in examples.
In the cellular automata simulation, the object under consideration is divided into small cells and the simulation is performed according to the local rule which is defined as the local relationship among cells. In this paper, the concept of cellular automata is applied to the design scheme of truss structures. First, truss elements are considered as the cells of the cellular automata and the local rule is derived from the optimization problem. The objective functions are defined to minimize the total weight of the structure and to obtain even stress distribution in the whole structure. The constraint conditions are introduced in order to define the local rule.
The present method is applied to the design of the plane and the three-dimensional truss structures such as Schwedler and Lamella Domes. The convergence histories of the total weight and the mean and the maximum stresses are shown in order to discuss the property of the present method.
Keywords: structural design, cellular automata (CA), local rule, truss structure.