A nonlinear static analysis of the sandwich plate using variational techniques and the Ritz method is presented. The kinematic description developed for a sandwich plate undergoing small strains and moderate rotations within the framework of Extended Higher Order Sandwich Panel Theory is considered. Employing the Ritz method, the total potential energy of the system is developed. Four different cases and combinations of boundary conditions are studied and assumed solutions satisfying the geometric boundary conditions are developed. The total potential energy results in nonlinear algebraic equations for the unknown coefficients in the assumed solution. The nonlinear equations are then solved using the Newton–Raphson method. A convergence study is then carried out to study the effect of variation of the number of terms in the assumed solution. In order to analyze the effect of inclusion of nonlinear effects in the core, results are computed considering only the facesheets with nonlinear strains and the core is considered to remain in the linear range. A stress analysis is carried out to compare the stresses predicted by the linear theory against the nonlinear results. After calculating and comparing the results for the simply supported case, three more cases for different sets of boundary conditions are also considered and presented. Since EHSAPT allows for analysis of plates with variable aspect ratios a further case where it is assumed that the depth of the plate is half the width is also considered and the results are presented for various geometric configurations.

提出了使用变分技术和Ritz方法对夹心板进行非线性静力分析的方法。考虑了在扩展高阶夹心板理论框架内为小应变和适度旋转的夹心板开发的运动学描述。利用Ritz方法，开发了系统的总势能。研究了边界条件的四种不同情况和组合，并提出了满足几何边界条件的假定解。总势能在假定解中导致未知系数的非线性代数方程式。然后使用牛顿-拉夫森（Newton-Raphson）方法求解非线性方程。然后进行收敛性研究，以研究假设解中项数变化的影响。为了分析在核心中包含非线性效应的影响，仅考虑具有非线性应变的面板来计算结果，并且将核心视为保持在线性范围内。进行了应力分析，以将线性理论预测的应力与非线性结果进行比较。在计算并比较了简单受支持情况的结果之后，还考虑并提出了三种针对不同边界条件集的其他情况。由于EHSAPT允许分析具有可变长宽比的板，因此还可以考虑另一种情况，即假定板的深度为宽度的一半，并针对各种几何构造提供结果。计算结果时仅考虑具有非线性应变的面板，并且将纤芯视为保持在线性范围内。进行了应力分析，以将线性理论预测的应力与非线性结果进行比较。在计算并比较了简单受支持情况的结果之后，还考虑并提出了三种针对不同边界条件集的其他情况。由于EHSAPT允许分析具有可变长宽比的板，因此还可以考虑另一种情况，即假定板的深度为宽度的一半，并针对各种几何构造提供结果。计算结果时仅考虑具有非线性应变的面板，并且将纤芯视为保持在线性范围内。进行了应力分析，以将线性理论预测的应力与非线性结果进行比较。在计算并比较了简单受支持情况的结果之后，还考虑并提出了三种针对不同边界条件集的其他情况。由于EHSAPT允许分析具有可变长宽比的板，因此还可以考虑另一种情况，即假定板的深度为宽度的一半，并针对各种几何构造提供结果。进行了应力分析，以将线性理论预测的应力与非线性结果进行比较。在计算并比较了简单支持情况的结果之后，还考虑并提出了三种针对不同边界条件集的情况。由于EHSAPT允许分析具有可变长宽比的板，因此还可以考虑另一种情况，即假定板的深度为宽度的一半，并针对各种几何构造提供结果。进行了应力分析，以将线性理论预测的应力与非线性结果进行比较。在计算并比较了简单受支持情况的结果之后，还考虑并提出了三种针对不同边界条件集的其他情况。由于EHSAPT允许分析具有可变长宽比的板，因此还可以考虑另一种情况，即假定板的深度为宽度的一半，并针对各种几何构造提供结果。