This paper develops tlie density under the Hausdorff measure,the definition of the density of fractal set under an outer-measure relating to dimension prints isgiven.

This model enables rapid approximate computation of the crack surface displacement and the crack front plastic zone size in the three-dimensional crack.

Using the Green’s functions,the extended general displacement solutions of three-dimensional crack problem in electro-magneto-thermo-elastic multiphase composites under extended loads are analyzed by boundary element method.

In this investigation,the fracture loads,absorbed energy of fracture,the displacement of application points of the loads,and the lengths of fiber cracks on fracture surfaces are measured in COD,four-point bending (4 PB),charpy V and three-point notch bending (3 NB) specimens of C-Mn steed and weld metal tested at the brittle-ductile transition temperature region.

Some specimens fracture after fiber cracks occurre and extend to various lengths and some specimens are unloaded prior to fracture.

3-D cracked J-integral formulas was transformed and treated by coordinate transformations,finite element and Gauss integral.

3-D crack of a compact tension(CT) specimen with concrete size is also analyzed.

By the algorithm, at first the volume data is transferred into the video RAM as 3D texture, then the ray s entry point, leave point and the ray traversal in the GPU are calculated by the vertex program and the fragment program.

The algorithm of texture mapping is dassified into two main categories,2D and 3D texture mappings.

At last this paper presents a comparison between 3d texture method and particle system of rendering cloud and smoke,to analyze the advantage of our me.