Research On Quadrilateral Grid Generation And Planarization For Free-form Grid Structures

For free-form surface grid generation,researches with some achievements have been made,which focus on triangular grids or quadrilateral grids non-coplanar.Compared with triangular grids,quadrilateral grids reduce the industrial processing of steel/glass plate and the number of rods.However,there are some trouble in application because of the non-coplanarity of quadrilateral grids.Based on the situation,the methods of generation and planarization for quadrilateral grids are studied.A quadrilateral grid generation method based on mapping is proposed.After dividing the boundary of the surface by dichotomy,the corresponding points of the parameter field are mapped back to the surface,connected in U and V directions.The results of quadrilateral grid generation are obtained.This method can complete the quadrilateral grids generation of free-form surfaces,but the quadrilateral grids are not coplanar.In order to solve the problem of non-coplanarity of quadrilateral grids,a quadrilateral planar grid generation method based on spring particle model(method 1)and a quadrilateral planar grids generation method based on surface constraint mapping(method 2)are presented.First,the traditional mapping method is applied to generate grids in method 1.Then according to the special requirements of different grid performances,the elastic coefficient kij,the boundary constraint stiffness kc,the adsorption stiffness km,and the planarity coefficient pc are calculated to establish the mesh spring-mass model.Finally,the coplanar grids are obtained by dynamic relaxation method through several iterations.In method 2,the surface is flattened into points based on the rule of minimum area variation firstly.Secondly the points are fitted into the two-dimensional plane,which is divided into quadrilateral grids.Then the two-dimensional mesh points are mapped to the surface under the constraint conditions with each mesh planarized.And the mesh points are iterated continuously until they converge or satisfy the requirement of planarization.On this basis,the planarization index,uniformity index and fluency index are proposed to evaluate the grids.The results show that,compared with the traditional mapping method,the planarization degree of the meshes obtained by the two methods is better.;Compared with method 2,method 1 has more universality and application prospects,which can be extended to quadrilateral and triangular hybrid grids with appropriate modification.