Three-dimensional Tetrahedral Mesh Generator Of KMAS And Study Of Corresponding Theories

With the rapid development of automobile industry recent years inChina, whereas the panel die as the key of automobile production inour nation is still lag behind. Compared with any other foreign country,the using life of the die in our country can be got only 1/3 to 1/5 ofother countries's. Every year our nation spends more than hundredsmillion dollars to replace the die instruments. Now, KMAS, whichregarded as the most superior CAE software , has a will to solve thisproblem. In fact, there are many elements involved in the using life ofthe die. One of the most important is to design die's structure well.Without the finite element calculation, we can't get good die structuredesign. The rapid development in computer software and hardware inthe last century's 80s, the finite element calculation can be finished byusing computer. The first step of using finite element technology toanalysis the pressure. One of the important steps is to disperse themodel to be tetrahedral mesh. The work of this step often occupied40% -50% of all finite element analysis working. Only done it well,the work following can get highly accurate results.As the previous research would be made by KMAS, this paper isfocusing on the design of three-dimensional model tetrahedral meshdisperse arithmetic, then making program for them. There are twomainly thinking on three-dimensional model tetrahedral mesh disperse,one is Delaunay triangulation method, the other is Advancing Frontmethod. The thinking of Delaunay is to use some method to makenodes inside the model, then according to Delaunay's rules link thesenodes, finally form the mesh. The thinking of Advancing Frontmethod is to work along the boundary of model towards inner side,gradually with some method, every time there is a node be made,linking node with mesh generated before to form the new meshelement, digging the model empty step by step, at last an overall meshgenerated. There are many arithmetices aroused by these two thinking.This paper adopted the classic Bowyer-Watson arithmetic, but as youknow, the Bowyer-Watson arithmetic doesn't act toward the controlledmodel, the so-called controlling means that the model which is readyto be dispersed has boundary, including the side of the boundary andthe surface of the boundary, so we must make some revisal onBowyer-Watson arithmetic. In order to let it fit the controlledcondition. The measured we taken are as followings:One, form the surface triangle mesh of model, which is ready to bedispersed. This paper adopted KMAS's grid generator to finish thisstep. Two, form the rough grid of model, which is ready to be disperse.First of all, we should form the initial five tetrahedral mesh elements,next using the surface nodes, which we made at the first step, insertingthe node one at a time to generate new tetrahedral mesh element.Nodes inserting arithmetic is: Finding the circum-sphere in theoriginal tetrahedral, including the tetrahedral, which is ready to befilled in the nodes. Construct the antrum of Delaunay, linking thereadied node and the nodes existed in the surface of Delaunay'santrum. Finally, delete the tetrahedral element, which connected theoutside of the model and eight nodes in the corner, in order toconstruct the original rough grid of the model's convexity. Three,Construct the inner nodes of the model, which is ready to be dispersed,this paper adopted the grid construct nodes method. Four, link nodesto form the tetrahedral mesh. It also use the nodes inserting arithmetic,whereas the difference is that every time the new tetrahedral elementformed, we should judge whether it followed Delaunay's rules, whichmeans that whether it's circum-sphere includes any other nodes. If theanswer is yes, then we can use the partial change method to changethem. As a result, the tetrahedral mesh which formed in the end,followed the Delaunay's rules well. Five, repair model restriction.Because of the using of partial change method, obviously thephenomenon that some model restriction losting will appear. We mustrepair restriction, including restrict sides and restrict triangle faces. Torepair the sides is quite easy, we can find the losted restrict sides easily,then repair them;however the repairation of the face is much morecomplex. The method we taken here is that: Finding the lost restrictface, following the rules, formed a new nodes, researching for thetetrahedral, which includes this nodes in the circum-sphere, linking itwith the lost restrict face to construct Delaunay antrum and generate anew tetrahedral.After the nodes has been made, to assure its quality and keep itsmoothing. We still need to do something important, Such as sliverdeletion and smoothing. Sliver is a tetrahedral which four vertexesalmost on the same plane. The deletion method, we adopted theCanvendish's partical change method. Smoothing originatedfrom the quality of mesh on some positions are far from satisfy, so wehave to do some adjustment on the position of the nodes on mesh toimprove the quality of it and make the transition more smoothing. Themost popular smoothing methods are nodes relaxation method andenergy method. The theory of the first method is to move the nodes ofthe mesh reasonably to improve the quality of it;the latter oneconsidering all the nodes as parameter and using original mesh modeldefines is energy function in the whole, Restricting this minimumvalue of the function to adjust the nodes of the mesh. Adopted theenergy method, we have to accumulate as much as possible, it's alsodifficult to control the partical shape. Based on these reasons, thispaper adopted nodes relaxation method to accomplish the smoothingof the mesh. Many ways we can use to reach the goal. According tonodes relaxation method, one of the most famous is Laplaciansmoothing method. It got extremely succeed in the instance oftwo-dimensional mesh. Under the instance of three-dimension,sometimes the moving of the nodes may affect the quality of the grid,even make it into a worse status. At times it will arouse the negativevolume phenomenon of mesh. According to the reasons I mentionedabove, this paper adopted the smoothing method on trials fromVenkatakrishnan to solve this problem perfectly.Through the methods and measurements we talked above, thetetrahedral mesh we get at last, can accomplish the calculation on thefinite element calculation much better than we expected, the satisfiedresults can we get. It fits well for our design request.