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By Song Q., Zhang Y.

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The great advantage of FMM is that the global stiffness matrix can be evaluated in parallel with respect to each node through the node-wise manner, and only satellite node information is required with each nodal calculation. Finally, a derivation of the solution is performed as the usual FEM. Thus, the FMM is a node-wise FEM, which still keeps the well-known excellent features of the usual FEM. The features of FMM are summarized as follows, (1) Easy to generate a large-scale mesh automatically (2) Processed without being conscious of mesh generation (3) The result being equivalent to that of the FEM DERIVATION OF ENRICHED FREE MESH METHOD On the other hand, "Assumed strain on the clustered local elements" is the concept of the EFMM: a revised version of the FMM, as shown in Fig.

The computational model is — 30 — shown in the left of Fig. 25. 3,000 cracks are distributed in a square region, and the number of DOF is 900,000. The truncation number of Taylor series is 20. Total CPU time cost is 6 hours 9 minutes. The right of Fig. 25 shows the COD results of a part of the whole region. 8GHz and 1GB memory. ^2^:^^^ — / Figure 25: 3000 randomly distributed cracks in a square region of 2D infinite space (left) and COD of cracks in a part of region (right) 2. Verification of the accuracy and efficiency of the FMDBEM Because the conventional boundary elements are inadequate to meet the square root displacement variation near the crack tip, a spherical crack tip element incorporating the displacement variation by modification of the shape functions is employed.

The following deals with solids and structures as deformable systems represented by finite elements. The response to applied actions is defined by the TV displacements of the mesh nodal points of the discretized object, in the TV x 1 vector u(z). It is considered in dependence of a set of/? design parameters in the p x 1 vector z = {z\ • • -zp} which are disposable in optimization. Optimum design will be attempted by minimizing a scalar objective function which defines the posed requirements: /0(z)=/[u(z),z].

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