The MPM eliminates difficulty with mesh distortion as in the Lagrangian method,and with interface tracking and nonlinear convection term as in Eulerian scheme.

Meshless methods are developed based on the finite element method, which establish trial function independent of elements, thus they have some advantages to solve nonlinear mechanical and crack propagation problems, because of effectively abstaining from complex meshing and disadvantageous influence of elements distorting.

MARC\Superform to simulate seamless steel tube continuous rolling process,it is difficult to measure the tube wall-thickness in post processing because of serious distortion of FE mesh.

So, unlike the Lagrangian formulation, ALE finite element can't cause the entanglement and degeneration of the mesh, and can describe accurately the free surface of the material during the processes, which is impossible in the Eulerian FEM.

Comparing with conventional numerical methods, the advantage of Meshless methods lies in its approximation based on nodes. The main feature of the methods is that mesh can be eliminated wholly or partly, and reducing difficulty in mesh generation of the structure, and not like the traditional method in which mesh generation can be a very time-consuming and expensive task.

Standard finite element approaches are still ineffective in handling extreme material deformation, such as cases of large deformations and moving discontinuities due to severe mesh distortion.

A method for controlling mesh distortion during the shape optimization process is given based on an explicit limit on the design change to prevent the Jacobian from vanishing.

It is shown that the mesh distortion that exists in the finite element-based design approach is effectively resolved for large shape changing design problems through 2-D and 3-D numerical examples.

On the other hand, the Eulerian formulation, with its fixed coordinate system, does not suffer from mesh distortion.

This is because the former does not only possess the same accuracy as the latter when regular meshes are employed for analysis, but is also very insensitive to mesh distortion, for which the Q8 element can not handle.

The strategy uses as input the grid distortion data, which provides the magnitudes of macroscopic particle velocities at discrete (nodal) points.

First, a plane channel flow at Reτ = 395 was simulated using both Cartesian and curvilinear grids; the results show that the model formulation is consistent and insensitive to grid distortion, and compares well with the reference data.

The association between Snellen visual acuity, Amsler grid distortion and presence of diabetic retinopathy with self-reported functioning and well-being (SF-36) were examined in a sample of 327 diabetics from the Medical Outcomes Study (MOS).

There was little or no correlation between Snellen visual acuity, Amsler grid distortion or diabetic retinopathy and functioning and well-being (i.e.

Maximum product-moment correlation was 0.15 with worst eye visual aculty, 0.13 with best eye visual acuity, 0.08 with presence of retinopathy, and 0.10 with Amsler grid distortion.

In this paper a comparison between superplasticity and non-superplasticity o the matreial Zn-22％ Al has been made through the alloy deformations in the process of extrusion and in that of upsetting, their hardness distribution and lattice variation measured practically, and their microstructure in the deformation area analyzed. The results show that the superplastic characteristics of the alloy deformation are different obviously from the non-superplastic characteristics owing to the effects of sensitivity strengthening...

In this paper a comparison between superplasticity and non-superplasticity o the matreial Zn-22％ Al has been made through the alloy deformations in the process of extrusion and in that of upsetting, their hardness distribution and lattice variation measured practically, and their microstructure in the deformation area analyzed. The results show that the superplastic characteristics of the alloy deformation are different obviously from the non-superplastic characteristics owing to the effects of sensitivity strengthening of the superplastic strain rate and thef boundary viscous friction in the alloy. It was observed that the superplastic deformation area in the alloy was distinct when it was extruded and invertedly extruded, but the microstructure of different parts remained unvaried. The alloy wsa deformed either by extrusion or by upsetting, the superplastic hardness would be higher than the non-superpla tic hardness due to the effect of strengthening of the superplastic fine grain dispersion. And the curvature radius of the barrelling in superplastic deformation of the alloy by upsetting was larger than that in nonsupcrplastic deformation of the alloy by upsetting.

An integrated system FSOP2D,including modules for the shape optimal modeling,structural analysis,sensitivity analysis,optimal method library and post- processing,is developed.By selecting fictitious loads as the design variables that has a linear relationship with the grid point locations and using design sensitivity analysis of the domain method,it is easier to solve the velocity field.In the course of optimal iterations,mesh distortion is kept to a minimum,sensitivity derivatives of object function,stress...

An integrated system FSOP2D,including modules for the shape optimal modeling,structural analysis,sensitivity analysis,optimal method library and post- processing,is developed.By selecting fictitious loads as the design variables that has a linear relationship with the grid point locations and using design sensitivity analysis of the domain method,it is easier to solve the velocity field.In the course of optimal iterations,mesh distortion is kept to a minimum,sensitivity derivatives of object function,stress constraints and displacement constraints are derived.Computation of sensitivity analysis is achieved in the system.Two engineering examples are used to prove the system's effectiveness,the optimal results can successfully be obtained by lesser number of iterations.

In numerical analysis many finite element models have acceptable performance when the computing meshes are regular. However, as the level of mesh distortion increases, their accuracy of solutions descends rapidly. Therefore, how to formulate an element that is less sensitive to geometric distortion was an important question for study for a long period. In this paper, a simple quadrilateral membrane element with rotational degrees-of-freedom is developed with the approach of the generalized conforming element...

In numerical analysis many finite element models have acceptable performance when the computing meshes are regular. However, as the level of mesh distortion increases, their accuracy of solutions descends rapidly. Therefore, how to formulate an element that is less sensitive to geometric distortion was an important question for study for a long period. In this paper, a simple quadrilateral membrane element with rotational degrees-of-freedom is developed with the approach of the generalized conforming element proposed earlier by one of the author of this paper. The new element exhibits an excellent feature, that is, much less sensitive to geometric distortion. Also a general method to formulate high precision finite element that is less sensitive to geometric distortion is provided in this paper.