Journal
APPLIED SCIENCES-BASEL
Volume 11, Issue 15, Pages -Publisher
MDPI
DOI: 10.3390/app11157159
Keywords
analytical solutions; beams; classical theory; shear deformation theories; functionally graded structures; modified couple stress; numerical results
Categories
Funding
- O'Donnell Foundation Chair IV at Texas AM University
- Distinguished Professorship at University of North Texas, Denton
- VAnviteLli pEr la RicErca'' by University of Campania Luigi Vanvitelli
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This review paper presents the governing equations and analytical solutions of the classical and shear deformation theories of functionally graded straight beams. The theories account for through-thickness material variation, strain gradient effects, and nonlinearity. Analytical solutions for bending, some of which are not commonly available, demonstrate the influence of material variation, boundary conditions, and loads.
This is a review paper containing the governing equations and analytical solutions of the classical and shear deformation theories of functionally graded straight beams. The classical, first-order, and third-order shear deformation theories account for through-thickness variation of two-constituent functionally graded material, modified couple stress (i.e., strain gradient), and the von Karman nonlinearity. Analytical solutions for bending of the linear theories, some of which are not readily available in the literature, are included to show the influence of the material variation, boundary conditions, and loads.
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