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Optimization of finite element mesh


Do a good unit composed of the grid. And its quality is not particularly good pass by some particularly bad unit and part of the failed unit consisting of mesh, which is obviously unreasonable. Second, this approach ignores the definition of particularly poor quality of the grid on the mesh quality group of cells plays a decisive impact. Then a class of over-emphasize the role of the worst unit is inappropriate. Undeniable. The worst accuracy of the calculation unit, in general, relatively larger. However. According to Saint-Venant principle, errors occurred mainly in the vicinity of the unit. In fact, in some calculations the model. Restrictions on the boundary geometry, in particular small corner units will have interior angles, this corner unit is often the worst in the entire grid cell. The internal structure may have a large number of substandard units is clearly not represented by a unit of the worst, especially in this little small-angle boundaries without load bearing and non-boundary conditions often the zero-stress state, real decision should be the accuracy of all the failure of other units. This unit is recommended that all failed to define the set of mesh quality, which failed to pass the grid at all levels within the unit cell of the small number of mesh quality is better. . Let the total number of grid cells, with that unit number (= 1,2, ..., m) the quality of the first units of measure for the first three Roth and military: Finite element mesh optimization method 69. Failed unit is the set of all S: IklQ> 1} (4) units will be set according to the quality of S's failure to make further distinction between the quality of this unit limits the introduction of sequence 0,1,2, a, z (5) where = 1. And the sequence is monotonically increasing that 0 },( f = 0, l, 2, ...,) (7) is clearly S is a subset of S, and there SuS} S2 ... S ( therefore can be a finite set S. Base, that is, the number of elements of its Card (S,) (i = 0, l, 2, ...,) to evaluate the quality of Agra. Specifically, the two can be compared based grid l and 2,[link widoczny dla zalogowanych], the quality of the same cell line sequence (5) the set of failed units were Sl: {JlQl> {S2: t�� lQ2>}, (i = 0 , 1,2,[link widoczny dla zalogowanych], ...,) if the collection corresponding to the base of a (9) Card ��S. 1) �� Card (S2) (i = 0, l, 2. ...,[link widoczny dla zalogowanych],) (1O) 1 is the grid quality is better than or equal to 2, the quality of the grid, and only if the type of equality for all i have set up, the quality of the two Agger was equal. When the failed unit by the quality of the finer, that is, sequences (5) the value contained in the more difference between the values adjacent to the more hours, more rigorous evaluation of the mesh quality. But the practical applications often do not require very strict judge, and sometimes even just considering several close (usually take slightly less than the worst element quality measure) and the higher value is sufficient. 4, a grid optimized algorithms geometric definition of quality from the Bragg can be seen, the grid geometry optimization is a multi-objective optimization problem. Compared with the single objective optimization problems, multi-objective optimization problem solving much more complex, and with the goal of increasing the number, the problem will become increasingly complex. In the optimization process taking into account the often conflicting objectives, a solution is to target based on the order of importance, giving priority to the relative importance of the goal. In addition,[link widoczny dla zalogowanych], the grid geometry optimization, optimizing the impact of the variable is local, according to this feature, you can optimize the use of structural optimization in the division thought, the whole optimization problem into Agger a series of small local optimization within the scope of the problem, after repeated iterations. Quality tends to make the best Agger. Specific approach is to first node involving substandard units are sorted according to certain rules, and then sort the nodes in order to optimize, that is, solving a series of smaller optimization problems. All the nodes are sorted in optimized to complete the round of iteration, check whether the convergence, no convergence to the next round of iteration, until convergence. All references to the failed node cells sorted,[link widoczny dla zalogowanych], then the following formula to calculate the value of the corresponding node J: 70 units of Sichuan Union University (Engineering Science Edition), Volume 3, gi = �� (Q-1). (11) where J is the unit around the number of nodes. Q (k = 1. 2. ..., H) the quality of these units. Press in sequence, the node order. If no = 0. Indicates that the node around the unit are qualified unit, these nodes are not included in the ranking. Sort of the nodes. Order optimization. Optimization variables are optimized node J Il and the two coordinates.

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[link widoczny dla zalogowanych]

[link widoczny dla zalogowanych]

[link widoczny dla zalogowanych]