variable modulus of elasticity

One of the applications of the numerical method of boundary elements is the calculation of stresses and displacements on the external and internal boundaries of a non-homogeneous object. In industry, when two molten material are combined together, there is a possibility that the resulting material is non-homogeneous material. In this article, the formulation needed to solve the direct problem of calculating the stresses and displacements on the external and internal boundaries of a non-homogeneous body with variable modulus of elasticity is presented. The answers obtained from the numerical solution are compared with the ANSYS software and it can be seen that the error of the results obtained using the boundary elements method is less than 2% with the results obtained from the software, which indicates the good accuracy of the solutions obtained from the numerical method of boundary elements.

One of the applications of optimization methods is solving the inverse problems of identifying internal boundaries, estimating the mechanical properties of materials and etc. In most of the articles, due to the simplicity of the relationships, the cases where the material is a homogeneous body have been considered, But in industry, when two molten material are combined together, there is a possibility that the resulting material is non-homogeneous material.In this article, identifying the geometry of the irregular internal boundaries between three materials and estimating the mechanical properties is presented. The intermediate material has a variable modulus of elasticity. This problem has been studied by combining three methods of colonial competition algorithm, simplex and conjugated gradian method along with the numerical method of Boundary Elements Method. The effect of the type and hardness of the constituent materials of the non-homogeneous body and the effect of the geometry and position of the internal boudaries on the convergence have been investigated. The obtained results indicate the power and ability of the presented method to estimate unknown parameters.