Construction of physical cover approximation in manifold method based on least square interpolation

In manifold method,the accuracy of numerical solutions can be increased by using an arbitrary expansion of analytical solution or high order polynomials on the physical cover free from changing the computational mesh.However,the use of high order polynomials introduces a large number of extra unknowns and makes it difficult to apply boundary conditions.To overcome these deficiencies,the least square method is employed to construct the displacement interpolation on the physical cover.It provides a new approach to construct high order manifold element without increasing the degrees of freedom and the essential boundary condition can be imposed as easy as it is in conventional FEM.Examples of cantilever beams and Cook beams are presented to demonstrate the effectiveness and efficiency of the present method.