Abstract

We prove the existence of solutions to the boundary value problem of equilibrium of elastic shallow inhomogeneous isotropic shells with free edges in the framework of Timoshenko beam model. The research is conducted in arbitrary curvilinear coordinates. The boundary value problem is reduced to a nonlinear operator equation with respect to generalized displacements in a Sobolev space. The solvability of the operator equation is established with the help of the contraction mapping principle.

中文翻译：

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曲线坐标下Timoshenko型浅壳非线性平衡问题的可解性

摘要

证明了Timoshenko梁模型框架下具有自由边的弹性浅层非均匀各向同性壳平衡边值问题解的存在性。该研究是在任意曲线坐标下进行的。边值问题被简化为关于 Sobolev 空间中广义位移的非线性算子方程。借助收缩映射原理建立了算子方程的可解性。