A new meshfree method for modeling strain gradient microbeams

The incapability of classical elasticity theory of accurately modeling the deformation behavior of structures at micro- and nanoscales has necessitated the development of more advanced theories. The strain gradient theory, being one of such theories, involves higher-order spatial derivatives of the field variables. However, except for few cases, there exists no analytical solution based on the strain gradient theory. This paper proposes a novel meshfree method with modified point interpolation functions possessing the Kronecker delta property; it is proposed to incorporate the strain gradient formulation into the Euler-Bernoulli beam theory. In the present method, the continuity of the shape function and its higher derivatives, appearing in the general form of the strain gradient theory, can be much more conveniently accommodated compared to the FEM. In addition, the present approach is based on the global weak form which is computationally less costly as compared to meshfree methods based on local weak form. The validity of the method is demonstrated by comparing the results with both analytical and experimental results for beams at macro- and microscales for static and dynamic loadings.