热环境下含切口和裂纹的功能梯度材料板的振动
Vibration of functionally graded material plates with cutouts & cracks in thermal environment
AI总结：
采用扩展有限元法研究热环境中含中心切口（圆形和椭圆形）及裂纹的功能梯度材料板的自由弯曲振动特性，分析了板几何、切口形状、裂纹长度、热梯度和边界条件的影响。
摘要：
本文研究了热环境中含中心切口（圆形和椭圆形）及从切口延伸的裂纹对功能梯度材料板自由弯曲振动行为的影响。利用单位分解法框架，不依赖网格表示不连续面。使用Heaviside函数捕捉不连续面上的位移跳跃，并使用渐近分支函数捕捉裂纹尖端的奇异性。采用富集剪切柔性4节点四边形单元进行空间离散。假设材料属性仅沿厚度方向变化。使用Mori-Tanaka均匀化方案估算功能梯度材料的有效属性，板运动学基于一阶剪切变形理论。数值研究了板几何、切口几何、裂纹长度、热梯度和边界条件对自由弯曲振动的影响。
英文摘要：
In this paper, the effect of a centrally located cutout (circular and elliptical) and cracks emanating from the cutout on the free flexural vibration behaviour of functionally graded material plates in thermal environment is studied. The discontinuity surface is represented independent of the mesh by exploiting the partition of unity method framework. A Heaviside function is used to capture the jump in the displacement across the discontinuity surface and asymptotic branch functions are used to capture the singularity around the crack tip. An enriched shear flexible 4-noded quadrilateral element is used for the spatial discretization. The properties are assumed to vary only in the thickness direction. The effective properties of the functionally graded material are estimated using the Mori- Tanaka homogenization scheme and the plate kinematics is based on the first order shear deformation theory. The influence of the plate geometry, the geometry of the cutout, the crack length, the thermal gradient and the boundary conditions on the free flexural vibration is numerically studied.
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