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In this paper, we show that the decomposition of the biharmonic equation into two Poisson equations is applicable to the general case of boundary conditions and any shape of the boundary edge of the plate, if we use the Local Integral Equation (LIE) formulation and a meshless approximation for primary field variables. Moreover, the spatial dependence of the bending stiffness does not give rise to any difficulties in this formulation. Such a formulation enables us to decrease the order of the derivatives of the field variables and so to increase the accuracy of numerical solutions. The efficiency and accuracy of several formulations is discussed in numerical tests using two alternative meshless approximations.

Meshless implementations of Local Integral Equations for bending of thin plates