| OCR Text |
Show the change in element density more gradual, nonuniform subdivision may be more numerically desirable, i.e., biased toward the rate of change in vari~tion of the subdivision criteria. 3. Subdivisions along all parametric directions: This implementation subdivides the element geometry into four subsurfaces even if the result variation along one of the parametric directions dominates the other. Selective subdivision may save a significant amount of time and space, but then the complexity of the underlying software may increase significantly as well. 4. Preliminary subdivisions: This is an automatic zoning process which programs the preliminary subdivisions with respect to the aspect ratio. The raison d'etre is that too long, skinny elements usually cause numerical instabilities (in numerical integration, for instance). Perhaps the aspect ratio can be considered as one reason to trigger further subdivision of the element geometry. 5. Energy criterion : The strain energy distribution is adopted as the only subdivision criterion in this implementation. However. this adaptive algorithm does not repudiate any other choices of criteria so long as the analysis result can be improved by means of element subdivision. 48 For some analysis codes, the element configuration resulting from sub-division might violate its configuration constraint. For example, Adina has fixed configuration in elements with 5 to 8 nodes in two-dimensional solid elements [2], and each such element can have no more than one intermediate node along each side. An anomaly occurs when an element has an adjacent sibling from subdivision having two or more levels of subdivision than itself, in which case the configuration constraint is violated. In this implementation, such oc-currences are detected and fixed by further subdividing the involved element to level with its neighboring elements. In this implementation, all the optimized meshes are derived from the very same initial, uniform mesh. An assumption is made that the initial mesh, though relatively coarse. should have captured all the possible areas w ith energy concentration, since otherwise, the element subdivision process will be insensitive to the omitted area however small the prescribed epsilon would be. This is because the criterion surface is constructed to represent only those |
