Starting from the three-dimensional theory of linear elasticity, we arrive at the exact plate problem by the use of Taylor series expansions. Applying the consistent-approximation approach to this problem leads to hierarchic generic plate theories. Mathematically, these plate theories are systems of partial-differential equations (PDEs), which contain the coefficients of the series expansions of the displacements (displacement coefficients) as variables. With the pseudo-reduction method, the PDE systems can be reduced to one main PDE, which is entirely written in the main variable, and several reduction PDEs, each written in the main variable and several non-main variables. So, after solving the main PDE, the reduction PDEs can be solved by insertion of the main variable. As a great disadvantage of the generic plate theories, there are fewer reduction PDEs than non-main variables so that not all of the latter can be determined independently. Within this paper, a modular structure of the displacement coefficients is found and proved. Based on it, we define so-called complete plate theories which enable us to determine all non-main variables independently. Also, a scheme to assemble Nth-order complete plate theories with equations from the generic plate theories is found. As it turns out, the governing PDEs from the complete plate theories fulfill the local boundary conditions and the local form of the equilibrium equations a priori. Furthermore, these results are compared with those of the classical theories and recently published papers on the consistent-approximation approach.

从线性弹性的三维理论开始，我们通过使用泰勒级数展开来得出精确的板问题。将一致近似方法应用于此问题将导致层次通用板理论。在数学上，这些板理论是偏微分方程（PDE）系统，其中包含位移的级数展开系数（位移系数）作为变量。使用伪归约方法，可以将PDE系统还原为一个完全写在主变量中的主PDE，以及几个还原PDE，每个归约PDE都写在主变量和几个非主变量中。因此，在求解主PDE之后，可以通过插入主变量来求解归约PDE。作为通用平板理论的一个重大缺点，与非主变量相比，归约PDE较少，因此并非所有的主变量都可以独立确定。在本文中，找到并证明了位移系数的模块化结构。在此基础上，我们定义了所谓的完整板理论，该理论使我们能够独立确定所有非主要变量。还有一个组装方案从通用板块理论中找到带有方程的N阶完整板块理论。事实证明，来自完整板理论的控制PDE先验地满足了局部边界条件和平衡方程的局部形式。此外，将这些结果与经典理论和最近发表的有关一致逼近方法的论文进行了比较。