In this work, we considered the new parametrization of a multilayer thin domain. In particular, in contrast to classic approaches, we used several base surfaces and an analytic method with the application of orthogonal polynomial systems. We gave the vector parametric equation of each layer and the system of vector parametric equations of a multilayer thin domain and introduced the geometric characteristics for the proposed parametrization. We also derived the expressions for the transfer components of the second-rank identity tensor and the relations connecting the various families of bases and presented some differential operators, the system of equations of motion, the heat flow equation, the constitutive relations of the theory of the micropolar elasticity, and the Fourier heat conduction law under this parametrization of the thin-body domain. Finally, we gave the classification and statements of boundary value problems in the theory of thin bodies.

中文翻译：

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多层薄体的建模

在这项工作中，我们考虑了多层薄域的新参数化。特别是，与经典方法相比，我们使用了多个基本曲面和一种应用正交多项式系统的解析方法。我们给出了每一层的矢量参数方程和多层薄域的矢量参数方程系统，并介绍了所提出的参数化的几何特征。我们还推导了二等式张量传递分量的表达式以及连接各个基族的关系，并给出了一些微分算子，运动方程组，热流方程，热力学理论的本构关系。在薄体区域的这种参数化下，微极性弹性和傅立叶热传导定律。