2D accurate solutions for the orthotropic plate under normal load. (September 2018) - Hou, Peng-Fei; Chen, Jia-Yun
Highlights: The whole stress field of an orthotropic plate under a normal line force is obtained. The solution is expressed explicitly in terms of elementary functions, therefore, it is convenient to be used in further study. Its application is not limited with the thickness of plate. Based on this Green's function, the stress field of orthotropic plate under arbitrary normal distributed load can be obtained. Abstract: Composite materials are wildly applied in the engineering and a lot of them behave as orthotropic. An accurate and efficient method for the orthotropic plate will contribute to the accurate design and quality promotion of this kind of structure. In this paper, the 2D Green's function for the orthotropic plate loaded by a normal line force is derived at first. By virtue of the 2D general solution of orthotropic material, a series of new harmonic functions which contain undetermined constants are constructed. Inserting the harmonic function into the general solution, the corresponding elastic fields in the orthotropic plate are obtained. These undetermined constants can be determined by the boundary conditions and the equilibrium equations. Then, based on the superposition principle and the obtained Green's function, the solutions for the arbitrary distributed normal loads can be obtained. At last, numerical analysis is presented to discuss the accuracy and efficiency of this method and the stress distribution in an orthotropic plate loaded by the normal loads are studied. Graphical abstract: Image, graphical abstract