Abstract A generalization of physically-based fixed degrees of freedom 3-D zig-zag theories is developed, which allows for any arbitrary choice of layerwise and representation functions. Thereby users can choose arbitrarily the representation case-by-case. This paper aims to prove that the choice of global and layerwise functions is immaterial whenever coefficients are recalculated exactly (via symbolic calculus) by the enforcement of interfacial stress continuity, boundary conditions and equilibrium in point form, as prescribed by the elasticity theory. Vice versa, accuracy of theories partially fulfilling constraints will prove to largely depend on the assumptions made and to be inadequate when strong layerwise effects rise, under distributed/localized step loading and boundary conditions other than simply supported edges (tests carried out in closed-form). The present and previous authors’ theories are tested with the aim to understand in which cases an adequate level of accuracy is still achieved by lower-order theories that are derived as particularizations.

中文翻译：

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关于基于 3-D 物理之字形理论的分层和全厚度全局函数选择的考虑

摘要 开发了基于物理的固定自由度 3-D 之字形理论的推广，它允许任意选择分层和表示函数。从而用户可以根据具体情况任意选择表示方式。本文旨在证明，只要通过执行弹性理论规定的界面应力连续性、边界条件和点形式的平衡来精确地重新计算系数（通过符号演算），全局函数和分层函数的选择是无关紧要的。反之亦然，部分满足约束的理论的准确性将被证明在很大程度上取决于所做的假设，并且当强大的分层效应上升时是不够的，在分布式/局部阶跃载荷和边界条件下，而不是简单支撑的边缘（以封闭形式进行的测试）。测试当前和以前作者的理论的目的是了解在哪些情况下仍然可以通过作为特殊化导出的低阶理论来实现足够的准确性。