Static analysis of functionally graded composite beams curved in elevation using higher order shear and normal deformation theory

Numerical Analysis of Thick Isotropic and Transversely Isotropic Plates in Bending using FE Based New Inverse Shear Deformation Theory

“…where i, j=1, 2, 3.., and , is in-plane force and bending moments resultants respectively correspondingly termed as stress resultants shown in Figure 2, while , , are extensional, coupling and bending moment stiffness matrices respectively, whereas 0 are membrane and curvature strains. Equation (7) shows a set of moment-curvature associations based on an implicit general stress field along the thickness derived by integrating the various stresses along with the depth of domain.…”

“…The comprehensive reviews of various refined theories [6] and a new hypothesis for the plate are used for thick plate vibration study through the thickness of the plate. The material properties fluctuate according to the power-law distribution [7], and the concept of virtual work is employed to derive the governing equations and model parameters in this theory. Navier's solution approach is used to solve simply supported curvature in elevation beams.…”

Effect of porosity on free vibration of functionally graded porous beam based on simple beam theory

“…Among three kinds of structure like beam, plate and shell, beam has always considered the interests of researchers because of its applications. There are many different beam theories used to analyze beam structures like simple beam theory [14][15], classical beam theory [16][17], first-order shear deformation theory [18][19] or higher-order shear deformation theory [20][21][22]. However, using a simple model helps us to reduce the computational cost with the resulting error within the allowable range.…”

Three Kinds օf Porosity օn Functionally Graded Porous Beams

“…There are three types of structure, like beam, plate and shell, but researchers are usually interested in beam structures because of its wide applications. Furthermore, many different beam theories were used to analyze beam structures, like simple beam theory [13], classical beam theory [14,15], first-order shear deformation theory [16][17][18][19][20] or higher-order shear deformation theory [21,22]. However, using a simple Timoshenko beam model helps us to reduce the computational cost with the resulting error within the allowable range.…”