A digital systematization of meshfree method and its applications to elasto-plastic infinitesimal deformation analysis

Topology synthesis of thermomechanical compliant mechanisms with geometrical nonlinearities using meshless method

“…It is emphasized that B 2 is a function of the nodal displacement u in nonlinear Eq. (18). The temperature change can be gotten by Eqs.…”

“…(12) and (1), and substituting the temperature change into Eqs. (18), we can obtain the displacement vector U 2 via Eq. (1).…”

“…Assuming that Eqs. (14) and (18) have been found, then the term k T 1 R 1 and k T 2 R 2 is equal to zero and the objective function can be written as…”

“…(14) and (18) have been found (R 1 = 0 and R 2 = 0).In order to get rid of the terms including od 1 /ox j and od 2 /ox j , those terms in Eq. (22) are set to zero, as…”

“…For compliant mechanisms of geometrical nonlinearity, the numerical accuracy will sometimes be seriously degenerate when the distortion of the elements exceeds the admissible error to cause the inconsistent mesh grids. To overcome this limitation, a family of new numerical methods, the meshless methods [18,19] can provide us with much convenience to effectively handle problems which may experience numerical difficultly when the standard FEM is employed.…”