Extended meshfree analysis of transverse and inplane loading of a laminated anisotropic plate of general planform geometry

摘要

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.