Abstract Three methods of approximation of lower non-differential terms in equations of dynamic problems of mechanics of deformable solids are studied with the use of explicit algorithms of the numerical solution based on several local approximations of each of the sought functions by linear polynomials. Additional equations based on the energy conservation law are formulated in the course of algorithm construction. The properties (dissipativity, monotonicity, and stability) of the proposed schemes are studied. Results of the numerical solution of the problem of deformation of an elastic plate with constant shear strains over the plate thickness (Timoshenko model) are presented. Results of the numerical solution of the problem of deformation of an elastic disk under pulsed loading are compared with the analytical solution of this problem.

中文翻译：

---

弹性体在脉冲载荷作用下变形问题的数值求解

摘要 使用基于线性多项式对每个所求函数的若干局部逼近的数值解的显式算法，研究了可变形固体力学动力学方程中低非微分项的三种逼近方法。基于能量守恒定律的附加方程是在算法构建过程中制定的。研究了所提出方案的特性（耗散性、单调性和稳定性）。给出了在板厚度范围内具有恒定剪切应变的弹性板变形问题的数值求解结果（Timoshenko 模型）。将脉冲载荷作用下弹性盘变形问题的数值解与该问题的解析解进行比较。