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A new, unified, theoretical framework for the formulation of general, nonlinear, single-scale shell theories

机译：一个新的，统一的理论框架，用于制定通用，非线性，单尺度壳理论

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摘要

A new, general theoretical framework for the generation of single-scale shell theories is presented. The framework is developed for application to the analysis of the general laminated and monolithic shells. The proposed framework is intended to allow the accurate prediction of the effects of material nonlinear-ity and wave propagation effects through the thickness of a shell. The starting point for the framework is a general, single-scale description of the displacement field expressed in terms of arbitrary expansion functions through the thickness of the shell. The functional forms and orders for the expansion functions in the displacement field representation are arbitrary. The development of the governing equations for the theory is carried out using the general nonlinear equations of continuum mechanics referenced to the initial configuration within the context of general coordinate systems. The equations of motion and the lateral surface boundary conditions for the theory are derived using the method of moments over the domain of the expansion functions. The (arbitrary) top and bottom surface boundary conditions (BCs) are satisfied exactly. The interfacial constraints (continuity of tractions and (dis) continuity of displacements) are also satisfied exactly. Delamination effects are incorporated into the theory through the use of arbitrary functions relating the displacement jumps to appropriate state variables. These functions can be changed without the need for reformulation of the governing equations. The theory is formulated in a sufficiently general fashion that any type of history-dependent material model can be used to describe the history-dependent behavior of the material composing a layer without the need to reformulate the theory. The theoretical framework is unified in the sense that any type of desired single scale shell (smear/ equivalent single layer (ESL), discrete layer, or zig-zag) theory can be obtained through suitable specialization of the framework. In the case of a smeared or ESL representation the domain of the displacement representation applies across the entire thickness of the shell. To generate a zig-zag theory within the context of the proposed framework is simply a matter of carrying out the interfacial analysis appropriate to the zig-zag assumptions and substituting the resulting displacement representation into the framework and then proceeding as with a smeared/ESL theory. In the case of a discrete layer analysis the displacement representations applies across each of the individual domains. The domains may correspond to several layers, a lamina, or a sublamina. Thus, the framework represents a comprehensive approach to modeling shells. The predictions of the theory are compared with the results obtained from an exact elastic solution for the static response of a sphere and the exact elastic solution for the dynamic response of monolithic sphere. Both exact solutions are based on the assumptions of spherically symmetric boundary conditions. It is shown that the theory is capable of providing accurate predictions for the pointwise (displacement, strain, and stress) fields distributions in laminated and monolithic shells. Furthermore, it is shown that the behavior of the theory is self-convergent and thus increasing the order of the analysis always converges the predictions to the correct answer.
机译：提出了一种新的通用理论框架，用于产生单尺度壳理论。开发了该框架，可用于分析一般的叠层和整体式外壳。提出的框架旨在允许通过壳的厚度准确预测材料非线性效应和波传播效应。框架的起点是对位移场的一般性单尺度描述，该位移场以通过壳的厚度的任意扩展函数表示。位移场表示中展开函数的功能形式和顺序是任意的。该理论的控制方程式的发展是使用连续统力学的一般非线性方程式进行的，该方程式是在一般坐标系的背景下参照初始构型的。该理论的运动方程和侧面边界条件是使用扩展函数域上的矩量法导出的。精确地满足了（任意）顶部和底部表面边界条件（BCs）。界面约束（牵引力的连续性和（位移）的连续性）也得到了精确满足。通过使用将位移跳跃与适当的状态变量相关联的任意函数，将分层效应纳入了理论。无需重新制定控制方程式，即可更改这些功能。该理论以足够普遍的方式制定，可以使用任何类型的历史依赖型材料模型来描述组成层的材料的历史依赖型行为，而无需重新制定该理论。理论框架是统一的，可以通过适当的框架专业化来获得任何类型的所需单刻度壳（涂片/等效单层（ESL），离散层或之字形）理论。在涂抹或ESL表示的情况下，位移表示的范围适用于壳体的整个厚度。要在提出的框架内生成锯齿形理论，只需进行适合于锯齿形假设的界面分析，然后将所得位移表示替换为框架，然后像涂抹/ ESL理论一样进行。在离散层分析的情况下，位移表示适用于每个单独的域。畴可以对应于几层，层或亚层。因此，该框架代表了一种建模外壳的综合方法。将理论的预测与从球体静态响应的精确弹性解和整体球体动态响应的精确弹性解中获得的结果进行比较。两种精确解均基于球对称边界条件的假设。结果表明，该理论能够为叠层和整体壳中的点状（位移，应变和应力）场分布提供准确的预测。此外，表明该理论的行为是自收敛的，因此增加分析的阶数总是使预测收敛到正确的答案。

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