Analysis of the Elastic Stress-Strain Behavior of Complex-Shaped Three-Dimensional Bodies

Abstract

The problem of the bending of a parallelepiped under external forces was examined using the finite element method. The given three-dimensional Lame equations were transformed into a symmetric algebraic system by applying the finite element method, and then solved using the square root method. As a result, the three displacements u1, u2, u3 and the six stress components σ11, σ22, σ33, σ12, σ13, σ23 were determined for various external forces and the height of the body. The formulation of three-dimensional elastoplastic problems, the application of finite element methods, Vlasov-Kantorovich, and finite difference methods in the calculation of bodies with complex three-dimensional shapes (with cavities, appendages, and depressions) is presented along with algorithms for solving the systems of equations and calculating the coefficients. By using a combination of theoretical analysis and numerical simulations, we study the interrelationship between elastic and plastic behaviors under various loading conditions. The research emphasizes the significance of the material properties, geometric configuration, and boundary conditions in influencing the modes of deformation.