Numerical modeling of bending, buckling, and vibration of functionally graded beams by using a higher-order shear deformation theory

Abstract

The objective of this work is to analyze the behavior beams functionally graded, simply supported, under different conditions such as bending, buckling, and vibration and this by use shear deformation theories a two-dimensional (2D) and quasi-three-dimensional (quasi-3D). The proposed theories take into account a new field of displacement which includes indeterminate whole terms and contains fewer unknowns, compared to other theories of the literature; by taking account of the effects of the transverse shears and the thickness stretching. In this theory, the distribution of the transverse shear stress is hyperbolic and satisfies the boundary conditions on the upper and lower surfaces of the beam without the need for a shear correction factor. In this type of beam the properties of the materials vary according to a distribution of the volume fraction, the Hamilton principle is used to calculate the equations of motion, and in order to check the accuracy of the theory used comparison is made with the studies existing in the literature.

Phân tích tĩnh tấm FGM có vi bọt rỗng trên nền đàn hồi Kerr theo lý thuyết biến dạng cắt bậc nhất đơn giản

“…[4], Hebbar và cs. [5], Thai và Vo [6], Chen và cs. [7], … Có nhiều mô hình tấm đã được sử dụng trong phân tích kết cấu tấm FGM, chúng đều xuất phát từ các lý thuyết áp dụng cho vật liệu đẳng hướng, sau đó mở rộng ứng dụng cho vật liệu composite, vật liệu FGM.…”

Free vibration analysis of the structural integrity on the porous functionally graded plates using a novel Quasi-3D hyperbolic high order shear deformation theory

“…Reddy et al [1][2][3] used thirdorder shear deformation theory to study the mechanical behavior of isotropic and FG plates and beams. Following that, several research projects have been carried out in order to develop new theories based on Reddy's theory (e.g., hyperbolictrigonometric [4][5][6][7][8][9][10][11][12][13], trigonometric [14][15][16][17][18], exponential [19], trigonometric-exponential [20], exponential-logarithmic [21], and polynomial [22][23][24][25]). Li et al [26][27][28] studied static and free vibration behavior of FG plates employing novel polynomial theories with shape parameter (m).…”

Lower bound estimate for buckling in axially graded cantilever rods

“…along the axial direction. Papers examining the instability of beams belonging to the first and second groups can be found in [14][15][16][17] and [18][19][20][21][22][23], respectively. The present paper exclusively considers the instability of axially graded cantilevers, belonging therefore to the second group.…”