The orthogonal meshless finite volume method for solving Euler–Bernoulli beam and thin plate problems

Elastostatic Deformation Analysis of Thick Isotropic Beams by Using Different Beam Theories and a Meshless Method

“…The SCF is used to compensate the error caused by the assumption of a constant transverse shear stress distribution along the beam thickness. The governing equations of the TBT is obtained in terms of generalized displacements by substituting equation (20) and equation (21) into equation (19),…”

Mixed Meshless Local Petrov-Galerkin Methods for Solving Linear Fourth-Order Differential Equations

“…In the primal meshless methods based on the weak forms of governing equations, additional degradation of computational efficiency in terms of computational time and numerical stability is caused by a problematic numerical integration of weak forms [8]. Later, Moosavi and others [9] used the mixed MLPG approach to derive a meshless counterpart of the mixed Finite Volume Method (FVM) [10] for the bending of thin beams.…”

“…Again, in contrast to FEM, the development of explicit strain gradient C1 models via primal Galerkin meshless methods is straightforward due to a high continuity order of meshless functions [15], but such approaches are also related to reduced accuracy due to the calculation of high-order derivatives of meshless functions [6]. In the mixed meshless approaches, complications may occur due to the improper imposition of boundary conditions [6] and due to solving large unsymmetrical global systems of equations [9]. At present, the focus has been shifted to the development of nodally integrated [16] and smoothed [17] meshless methods that avoid the integration of weak forms of governing equations as much as possible in order to reduce the computation time while obtaining the numerical stability and accuracy of the numerical method.…”

Flexure Analysis of Laminated Composite and Sandwich Beams Using Timoshenko Beam Theory

“…Meshless methods are the most promising and have attracted considerable attention for the analysis of engineering problems with intrinsic complexity. Meshless methods are widely used in static and dynamic analyses of the isotropic, laminated composite and functionally graded beam problems [15][16][17][18][19][20][21][22][23]. However, the studies are very limited regarding to the flexure analysis of laminated composite and sandwich beams by employing a meshless method [24][25][26][27].…”