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首页> 外文期刊>Archive of Applied Mechanics >Analytical solution of classical and non-classical boundary value contact problems of thermoelasticity for a rectangular parallelepiped consisting of compressible and incompressible elastic layers and numerical example of the solution of such problems
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Analytical solution of classical and non-classical boundary value contact problems of thermoelasticity for a rectangular parallelepiped consisting of compressible and incompressible elastic layers and numerical example of the solution of such problems

机译:包含可压缩和不可压缩弹性层的长方体热弹性的经典和非经典边值接触问题的解析解以及此类问题的数值示例

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The paper deals with a static thermoelastic equilibrium of an N-layer rectangular parallelepiped. The layers of the considered body are made of an isotropic homogeneous elastic material. A case when some of the layers consist of incompressible elastic materials, which are also assumed to be isotropic and homogeneous, is considered as well. Boundary conditions of symmetric or antisymmetric continuous extension of the solution are imposed on the lateral facets of the parallelepiped. Between the layers contact conditions of rigid, sliding or other type of contact can be defined. On the upper and lower facets of the parallelepiped, arbitrary boundary conditions are defined. Solution of the stated problems is made analytically using the method of separation of variables. The solution of the problems is reduced to the solution of systems of linear algebraic equations with block diagonal matrices. In the conclusion, a practical example establishing the elastic equilibrium of a three-layer rectangular parallelepiped is given.
机译:本文涉及N层长方体的静态热弹性平衡。所考虑的主体的各层由各向同性的均匀弹性材料制成。也考虑其中一些层由不可压缩的弹性材料组成的情况,该材料也被认为是各向同性的和均质的。对称或反对称连续扩展溶液的边界条件被施加到平行六面体的侧面上。在各层之间,可以定义刚性,滑动或其他类型的接触的接触条件。在平行六面体的上面和下面,定义了任意边界条件。所述问题的解决方案是使用变量分离的方法来分析地解决的。问题的解答被简化为带有块对角矩阵的线性代数方程组的解答。最后,给出了建立三层长方体弹性平衡的实例。

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