Abstract
A general method for solving all types of problems of “Solid mechanics” is given. A unified algorithm is proposed for solving the main types of problems of deformable solid mechanics: classical theory of elasticity, physically and geometrically nonlinear problems, dynamic problems of elasticity theory. A model of heat transfer in media with finite velocities is also proposed. The essence of the approach is to replace a continuous deformable medium with a system of interacting particles equivalent in physical and mechanical properties. The interaction potential between neighboring particles for an elastic isotropic continuous medium is determined by the Young’s modulus, Poisson’s ratio, or their analogues for heat transfer problems. The problems that must be solved for the effective use of a new method for solving problems of solid mechanics are outlined. Such a model is similar to dynamic models with concentrated masses, represented by systems of linear (or nonlinear) differential equations, algorithms and numerical methods for solving which are well known. However, it is necessary to ensure the accuracy of numerical integration and reduce the number of computational operations. It is proposed to use neural networks to solve large systems of ordinary differential equations. A mathematical analysis of the methods of separating a continuous medium and placing masses at points in an uneven grid of dynamic particles and a method for selecting a damping coefficient proportional to the velocity of movement of a material point is required.
Published Version
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