This study focuses on the stress analysis of imperfect functionally graded porous (FGP) sandwich beams using the Peridynamic Differential Operator (PDDO) and Refined Zigzag Theory (RZT). Functionally graded materials (FGMs) can be found in diverse engineering applications since they offer smooth transitions in the mechanical properties of distinct materials, unlike traditional composite materials. Micro-voids and porosities may appear inside the FGMs due to technical challenges during the manufacturing process of such materials. Therefore, understanding the stress variations of the FG sandwich beams with porosities/micro-voids, which are called imperfect FGMs, under loads is of vital importance. In order to achieve the porous configuration in the FG structures, the modified rule of mixtures is applied to calculate the effective material properties of FGMs. The RZT is very suitable for stress analysis of laminated composites, especially for thick and moderately thick beams. It contains only four kinematic variables and eliminates the use of the shear correction factors. In this study, the equilibrium equations of the RZT are solved by means of the PDDO for the stress analysis of imperfect FG sandwich beams having uniform and non-uniform porosity distributions. The PDDO transforms the differential equations into their nonlocal form, namely integral form, providing highly accurate approximations of the derivatives. A comprehensive PDDO analysis is performed for the investigation of the influence of the material variation, and even and uneven porosity distributions on the stress variations of the imperfect FG sandwich beams. It is noted that when the FG core exhibits soft material distributions, the effect of porosity is evident. The even type porosity distribution pattern is more influential on the axial displacement and stress variations in comparison with those of the uneven type porosity distribution pattern.

中文翻译：

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基于细化锯齿理论的不完美功能梯度多孔夹层梁应力分析的近场动力学微分算子


本研究重点使用近场动力学微分算子 (PDDO) 和细化 Zigzag 理论 (RZT) 对不完美功能梯度多孔 (FGP) 夹层梁进行应力分析。功能梯度材料 (FGM) 可以在多种工程应用中找到，因为与传统复合材料不同，它们可以实现不同材料机械性能的平滑过渡。由于此类材料制造过程中的技术挑战，FGM 内部可能会出现微空隙和孔隙。因此，了解具有孔隙/微空隙的 FG 夹层梁（称为不完美 FGM）在载荷作用下的应力变化至关重要。为了实现 FG 结构中的多孔构型，应用混合物的修正规则来计算 FGM 的有效材料性能。 RZT非常适合层合复合材料的应力分析，特别是厚梁和中厚梁。它仅包含四个运动学变量，并且消除了剪切校正因子的使用。在这项研究中，RZT 的平衡方程通过 PDDO 求解，用于对具有均匀和非均匀孔隙率分布的不完美 FG 夹层梁进行应力分析。 PDDO 将微分方程转换为非局部形式，即积分形式，提供导数的高精度近似值。进行了全面的 PDDO 分析，以研究材料变化以及均匀和不均匀的孔隙率分布对不完美 FG 夹层梁应力变化的影响。值得注意的是，当 FG 芯表现出软材料分布时，孔隙率的影响很明显。 与不均​​匀型孔隙分布模式相比，均匀型孔隙分布模式对轴向位移和应力变化的影响更大。