Differential quadrature buckling analyses of rectangular plates subjected to non-uniform distributed in-plane loadings

Elastoplastic buckling analysis of thick rectangular plates by using the differential quadrature method

“…The differential quadrature (DQ) method, proposed by Bellman and Casti [13] in 1971, is a numerical technique for the solution of initial and boundary value problems. Since the method was first used by Bert and his co-workers to solve structural mechanics problems in 1988 [14], the DQ method has been utilized successfully for analyzing a variety of linear and nonlinear structural mechanics problems [15][16][17][18][19][20][21][22][23][24]. The DQ method is used to solve the elastic buckling problem of plates with various combinations of boundary conditions and uniformly or non-uniformly distributed edge loadings [18][19][20][21], the elastoplastic buckling problem of thin rectangular plates under biaxial loadings [11], and the challenging problem of free vibration of curvilinear quadrilateral plates [22].…”

Discrete singular convolution approach for buckling analysis of rectangular Kirchhoff plates subjected to compressive loads on two-opposite edges

“…The analysis of vibration and buckling of plates has been the subject of the research of structural and mechanical engineering [18][19][20][21][22][23][24][25][26]. Long list of references and detailed formulation on buckling and vibration of rectangular plates are given, for example, in Refs.…”

Bending analysis of thin functionally graded plates using generalized differential quadrature method

“…The generalized differential quadrature method (GDQM) was first introduced by Shu and Richards [41] to simplify the calculation of the weighting coefficients and then used successfully by Shu and Wang [42] for the problems with mixed boundary conditions. Since the GDQM needs neither restriction on the distribution and number of discrete grid points nor solving a set of linear algebraic equations to compute the weighting coefficients, it has been applied in various cases of mechanical engineering problems [43][44][45][46]. In addition to the polynomial basis functions that used in the original GDQM [47][48][49][50], namely polynomial differential quadrature (PDQ) method, another approach for determining the weighting coefficients is using harmonic functions proposed by Striz et al [51] which has found extensive applications, as the harmonic differential quadrature (HDQ) method, for static and dynamic analysis of structures with arbitrary boundary conditions [52][53][54][55].…”