Graded finite elements are presented within the framework of a generalized isoparametric formulation. Such elements possess a spatially varying material property field, e.g. Young’s modulus and Poisson’s ratio for isotropic materials; and principal Young’s moduli in-plane shear modulus and Poisson’s ratio for orthotropic materials. To investigate the influence of material property variation, both exponentially and linearly graded materials are considered and compared. Several boundary value problems involving continuously nonhomogeneous isotropic and orthotropic materials are solved, and the performance of graded elements is compared to that of conventional homogeneous elements with reference to analytical solutions. Such solutions are obtained for an orthotropic plate of infinite length and finite width subjected to various loading conditions. The corresponding solutions for an isotropic plate are obtained from those for the orthotropic plate. In general, graded finite elements provide more accurate local stress than conventional homogeneous elements, however, such may not be the case for four-node quadrilateral (Q4) elements. The framework described here can serve as the basis for further investigations such as thermal and dynamic problems in functionally graded materials.
Isoparametric Graded Finite Elements for Nonhomogeneous Isotropic and Orthotropic Materials
Contributed by the Applied Mechanics Division of THE AMERICAN SOCIETY OF MECHANICAL ENGINEERS for publication in the JOURNAL OF APPLIED MECHANICS. Manuscript received by the ASME Applied Mechanics Division, July 2, 2001; final revision Nov. 14, 2001. Associate Editor: M.-J. Pindera. Discussion on the paper should be addressed to the Editor, Professor Lewis T. Wheeler, Department of Mechanical Engineering, University of Houston, Houston, TX 77204-4792, and will be accepted until four months after final publication of the paper itself in the THE AMERICAN SOCIETY OF MECHANICAL ENGINEERSJOURNAL OF APPLIED MECHANICS.
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Kim , J., and Paulino, G. H. (June 20, 2002). "Isoparametric Graded Finite Elements for Nonhomogeneous Isotropic and Orthotropic Materials ." ASME. J. Appl. Mech. July 2002; 69(4): 502–514. https://doi.org/10.1115/1.1467094
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