论文标题
关于薄壁结构的理论和实践
On the Theory and Practice of Thin Walled Structures
论文作者
论文摘要
当在弹性板和壳体的表面上给出一般性应力矢量时，我们考虑了边界条件满意度的问题。在广泛的理论和分层类型模型中，这两个问题也是开放的。 Vekua制定了用于分层模型的该模型。在非线性情况下，弯曲和压缩扩展过程没有分裂，为此，我们引用了von Karman型系统，而没有各种临时假设，因为在这种DES系统的经典形式中，其中一个代表了兼容性的条件，但它不是平衡方程。因此，我们在各向异性非均匀的弹性板和壳的线性和非线性案例中创建了精制理论的数学理论，大约满足了表面上部分微分方程和边界条件的相应系统。最佳且方便的理论可以通过选择任意参数轻松选择；在不使用任何简化的假设的情况下，已经进行了一些必要的实验测量。对于分层模型也解决了同样的问题。
We consider the problem of satisfaction of boundary conditions when the generalized stress vector is given on the surfaces for elastic plates and shells. This problem was open also both for refined theories in the wide sense and hierarchical type models. This one for hierarchical models was formulated by Vekua. In nonlinear cases the bending and compression-extension processes did not split and for this aim we cited von Karman type system without variety of ad hoc assumptions since, in the classical form of this system of DEs one of them represents the condition of compatibility but it is not an equilibrium equation. Thus, we created the mathematical theory of refined theories both in linear and nonlinear cases for anisotropic nonhomogeneous elastic plates and shells, approximately satisfying the corresponding system of partial differential equations and boundary conditions on the surfaces. The optimal and convenient refined theory might be chosen easily by selection of arbitrary parameters; preliminarily a few necessary experimental measurements have been made without using any simplifying hypotheses. The same problem is solved for hierarchical models too.
