The bending analysis of isotropic, laminated composite and cylindrical sandwich shells was carried out using a higher order shear deformation theory which incorporates undetermined integral in the displacement field. The model proposed involves only four variables. Moreover, unlike the conventional FSDTs, the shear correction factor is not necessary. The Hamilton’s principle and the Navier’s method are employed to determine and solve the equations of motion. The present analytical model was compared with other higher-order theories in the literature. In addition, finite element analysis methods were designed to calculate displacements and stresses of shells. Shells are subjected to uniform loads. Results are given for shallow and deep shells and thick to thin. According to the analysis, kinematics, based on the indeterminate integral component, are very effective and enable researchers to investigate laminated plates and shells more accurately than traditional models.

使用高阶剪切变形理论对各向同性、层合复合材料和圆柱形夹层壳进行弯曲分析，该理论在位移场中纳入了未定积分。提出的模型仅涉及四个变量。此外，与传统的 FSDT 不同，剪切校正因子不是必需的。采用汉密尔顿原理和纳维方法来确定和求解运动方程。将当前的分析模型与文献中的其他高阶理论进行了比较。此外，还设计了有限元分析方法来计算壳体的位移和应力。壳承受均匀载荷。给出了浅贝壳和深贝壳以及厚贝壳和薄贝壳的结果。根据分析，基于不定积分分量的运动学非常有效，使研究人员能够比传统模型更准确地研究层合板和壳。