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The local Petrov–Galerkin method (MLPG) is applied to solve the geometrically nonlinear problem in this paper. The local Petrov–Galerkin method uses the moving least square approximation as a trial function, and involves only integrations over a regular local subdomain and on a local subboundary centered at a node in question. These special properties lead to a more convenient formulation in dealing with nonlinear problems. An incremental and iterative solution procedure is used to solve the geometrically nonlinear problem. Formulations for the geometrically nonlinear problems are obtained from virtual work principle. All measures are related back to the original configuration. Several examples are given to show that the local Petrov–Galerkin method has good accuracy in solving the geometrically nonlinear problem.

Smoothed particle hydrodynamics (SPH) is extended to the strain rate independent elastic-plastic large deformation analysis for low velocity contact problems. The volume constant condition is imposed on the plastic deformation process using a pressure equation given by the particle density condition in a unit volume. Test problems show that these improvements lead to good stability and accuracy of large deformation analysis.

Two methods of stress recovery have been suggested and investigated in this paper. The first one is introduced by using moving least square method (MLS) and superconvergent points. The second method is based on the satisfaction of equilibrium equations at some nodes for which the recovery is applied. Simultaneous solution of these equations increases computational time. So, the second method is more expensive than the first one. A numerical example is used to compare the stresses recovered by these two methods with corresponding FEM, well-known SPR method and analytical solutions. The effect of various orders of basis functions and the values of weight functions on stress recovery by the proposed methods is also investigated. The present research indicates that the two methods, and especially the first one, represent acceptable accuracy over the domain and even on the boundaries, in comparison with SPR method, and also good convergency is achieved.

Partition of unity quadrature (PUQ) for Galerkin meshless methods is presented and Galerkin meshless methods based on PUQ are studied in detail. The mathematic foundations of PUQ, finite covering and partition of unity, are described and the validity of PUQ is proved theoretically. Galerkin meshless methods based on PUQ do not require any mesh information and are ’truly’ meshless methods. Numerical examples show the excellent agreement with conventional quadrature methods and exact solution, which exemplifies the accuracy and robustness of Galerkin meshless methods based on PUQ. The relation between accuracy of integral and cover size is also analysed.

This paper discusses a scheme for choosing local upwind biased support domains in the RPICM for solving convection-dominated problems. A numerical example of a 2D steady state convection-domainted problem is presented. It is demonstrated that significant improvement on the accuracy can be obtained after using this scheme for convection-dominated problems.

This paper describes a meshfree collocation procedure for heat transfer analysis. In this procedure, radial point interpolation method (RPIM) is employed to construct shape functions and a finite calculus treatment is used for problems with derivative boundary conditions to improve the stability and accuracy of numerical solution. Numerical examples of 2-D and 3-D heat transfer problems are presented to study the stabilization parameter to demonstrate the efficiency of the present numerical procedure.

Symplectic analysis is introduced into optical waveguide theory, by using Hamiltonian system theory in which the transverse electric and magnetic field vectors are the dual vectors. The method can accommodate arbitrary anisotropic material. The electro-magnetic stiffness matrix of a typical segment in optical waveguide is generated by means of the combination algorithm of contiguous segments based on energy variational principle. Then the Wittrick–Williams algorithm is used to extract the eigenvalues. Thereafter, an energy band analysis is performed for optical waveguide in layered media.

In this paper, based on the analysis of coupling action of temperature, phase transformation, magnetic field and stress, the phase transformation condition and equation related to material properties are discussed, a new constitutive equation considering effects of phase transformation and magnetic field is proposed and solved by means of Finite Element Method (F.E.M). The thermal residual stress is obtained and the influencing factors on the thermal stress of magnetic field are analysed and discussed.

This paper presents a parallel finite element analysis of high frequency electromagnetic wave in an environment. The HDDM (Hierarchical Domain Decomposition Method) is employed as a parallel solver. Nedelec element is employed. The simulation method is tested for a simple model, and the results are compared with exact solutions.

The continuous miniaturization of electronic products has led to new concerns over the resistance of interconnections between transistors. As transistors become smaller and consequently faster, delays in interconnects start to account for a considerable proportion of processing time. One solution is to replace the conventional Al/SiO interconnects with Cu/silk interconnects. In order to curb the diffusion of Cu into silk, it has been proposed to coat the Cu with Ta. The suitability of Ta as a diffusion barrier is still not fully established. Ab initio MD simulations were carried out to characterize the diffusion of Cu and Ta atoms inside silk-like polymer structures. The results showed that Cu is much more active in the silk-like polymer than Ta. An analysis of the speed of the Cu atom in the silk polymer showed that the Cu atom experienced impulsive interatomic loads. Such impulses are postulated to cause hoppings, which were highlighted in reports of previous classical MD simulations. In contrast, the motion of Ta atom was relatively stable and can be considered as harmonic oscillations around an equilibrium position. The ‘inert’ characteristic of Ta suggests it is a good material to serve as a barrier between copper and silk layers to prevent the leakage of Cu into silk.