Abstract. This paper presents the meshless local integral equation method (LIEM) for nonlocal analyses of two-dimensional dynamic problems based on the Eringen's model. A unit test function is used in the local weak-form of the governing equation and by applying the divergence theorem to the weak-form, local boundary-domain integral equations are derived. Radial Basis Function (RBF) approximations are utilized for implementation of displacements. The Newmark method is employed to carry out the time marching approximation. Two numerical examples are presented to demonstrate the application of time domain technique to deal with nonlocal elastodynamic mechanical problems.

In order to study the mechanical properties of the heterogeneous core plate of the wind turbine blade, a modeling method of the core plate based on displacement field variables is proposed. Firstly, the wind turbine blade core plate was modeled according to the theory of modeling heterogeneous material characteristics. Secondly, the three-point bending finite element model of the wind turbine blade core plate was solved by the display dynamic equation to obtain the deformation pattern and force-deformation relationship of the core plate. Finally, the three-point bending static test was conducted to compare with the finite element analysis. The test results show that: the damage form of the wind turbine blade core plate includes elasticity, yield, and failure stages. The main failure modes are plastic deformation, core material collapse, and panel-core delamination. The failure load measured by the test is 1.59 kN, which is basically consistent with the load-displacement result obtained by the simulation, with a difference of only 1.9%, which verifies the validity and reliability of the model. It provides data references for wind turbine blade structure design.

The analysis of sphere nonlocal elasticity is carried out by using the improved point collocation method. The approach is based on the Eringen’s model and two and three dimension problems are transformed to one dimension problems considering the polar symmetry. One dimension second order differential equation in terms of radial displacement is derived with domain integral. Due to the excellent accuracy of the point collocation method to one dimension differential equation using the radial basis function interpolation, the numerical solutions can be used as benchmarks. This approach can be easily extended to dynamic nonlocal elasticity and plasticity for sphere.

The fracture analysis for two-dimensional nonlocal elasticity is presented by the numerical approaches i.e. the Local Integral Equation Method (LIEM). Based on the Eringen’s model, the nonlocal stresses at the crack tip are regular. Numerical simulation by LIEM is proposed for the nonlocal elasticity fracture problems. A rectangular cracked plate subjected to tensile load is observed numerically to demonstrate the convergence and accuracy of LIEM.

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