An improved interpolating element-free Galerkin method for elasticity

Based on the improved interpolating moving least-squares （ⅡMLS） method and the Galerkin weak form, an improved interpolating element-free Galerkin （ⅡEFG） method is presented for two-dimensional elasticity problems in this paper. Compared with the interpolating moving least-squares （IMLS） method presented by Lancaster, the ⅡMLS method uses the nonsingular weight function. The number of unknown coefficients in the trial function of the ⅡMLS method is less than that of the MLS approximation and the shape function of the ⅡMLS method satisfies the property of Kronecker δ function. Thus in the ⅡEFG method, the essential boundary conditions can be applied directly and easily, then the numerical solutions can be obtained with higher precision than those obtained by the interpolating element-free Galerkin （IEFG） method. For the purposes of demonstration, four numerical examples are solved using the ⅡEFG method.

A numerical approach based on the meshless collocation method in elastodynamics

In this paper, a collocation technique with the modified equilibrium on line method （ELM） for imposition of Neumann （natural） boundary conditions is presented for solving the two-dimensional problems of linear elastic body vibrations. In the modified ELM, equilibrium over the lines on the natural boundary is satisfied as Neumann boundary condition equations. In other words, the natural boundary conditions are satisfied naturally by using the weak formulation. The performance of the modified version of the ELM is studied for collocation methods based on two different ways to construct meshless shape functions： moving least squares approximation and radial basis point interpolation. Numerical examples of two-dimensional free and forced vibration analyses show that by using the modified ELM, more stable and accurate results would be obtained in comparison with the direct collocation method.

Influencing Factors of Total Factor Energy Efficiency in Bohai Rim Region Based on DEA-Tobit Model

Bohai Rim region is an important economic development area and a large carbon emission area in China.It is of great significance to explore the total factor energy efficiency and its influencing factors for the low carbon transformation and high-quality development of the Bohai Rim region.Based on the total factor energy efficiency framework,the DDF-DEA model was used to calculate the total factor energy efficiency,and the internal and external differences of the total factor energy efficiency were further analyzed.The internal and external influencing factors were determined by ML index method and classical endogenous growth theory,and then the Tobit panel model was used to empirically analyze the action mechanism of all influencing factors of total factor energy efficiency in the Bohai Rim region.The results show that the pure technical efficiency,scale efficiency and technological progress among the internal influencing factors contribute to the improvement of energy efficiency in the Bohai Rim region.Industrial structure,industrial internal structure and ownership structure inhibit the improvement of energy efficiency.Energy consumption structure and energy endowment also have a negative impact on energy efficiency.Therefore,measures such as promoting technological progress,adjusting economic structure and optimizing energy structure will effectively improve total factor energy efficiency in the Bohai Rim region.