Extended meshfree analysis of transverse and inplane loading of a laminated anisotropic plate of general planform geometry
Extended meshfree analysis of transverse and inplane loading of a laminated anisotropic plate of general planform geometry
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DOI：
10.1016/j.ijsolstr.2005.03.068
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发表时间：
2006
影响因子：
3.6
通讯作者：
Dong-dong Wang;S. B. Dong;Jiun-Shyan Chen
中科院分区：
文献类型：
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作者：
Dong-dong Wang;S. B. Dong;Jiun-Shyan Chen
提出了一种分析各向异性层合板弹性静力问题的扩展无网格法。该板可以是任何平面形状，其厚度轮廓由不同各向异性材料的完美结合的均匀厚度层组成。横向和平面内的负载被认为是使用一阶剪切变形理论的弯曲行为和广义平面应力的膜的行为。在这种扩展的无网格法中，首先考虑矩形区域内任意几何形状的板，然后采用解析广义Navier解（复合双傅立叶级数）形式的特解来描述矩形区域内的载荷响应。然后，在板的实际轮廓上加入无网格分析的齐次解来处理增广边界条件。这些增广的条件是由规定的值和特定的解决方案评估周围的板的轮廓。集中的横向和平面内载荷的形式均匀载荷在一个非常小的补丁被认为是与此广义Navier解决方案表示。当一个无网格部分被添加到帐户的边界条件，这样的解决方案构成的绿色功能的板。这些双傅立叶级数表示的可行性所示的运动学和力/力矩场的收敛速度。最后给出了一个±30°角铺设双层圆板的算例，以说明该方法的有效性。
An extended meshfree method is presented for the analysis of a laminated anisotropic plate under elastostatic loading. The plate may be of any planform shape with its thickness profile composed of perfectly bonded uniform thickness layers of distinct anisotropic materials. Both transverse and inplane loads are considered using a first order shear deformation theory for flexural behavior and generalized plane stress for the membrane behavior. In this extended meshfree method, a rectangular domain is initially considered with the plate of arbitrary geometry inscribed within it. A particular solution in the form of an analytic generalized Navier solution (a compound double Fourier series) is used to capture the response due to the loading within the rectangular domain. Then, a homogeneous solution by meshfree analysis is added to treat the augmented boundary conditions on the actual contour of the plate. These augmented conditions are composed of the prescribed values and that of the particular solution evaluated around the plate’s contour. Concentrated transverse and inplane loads in the form of uniform loads over a very small patch are considered with this generalized Navier solution representation. When a meshfree portion is added to account for the boundary conditions, such solutions constitute the Green’s functions for the plate. The viability of these double Fourier series representations is shown by the convergence rates for the kinematic and force/moment fields. An additional example of a two layer ±30° angleply circular plate is given to illustrate the capability of this extended meshfree method.