Research On Morphogenesis Technique For Free-form Surface Structures Considering Geometrical Nonlinearity

With the development of social economy,the traditional structure form can not satisfy people's aesthetic requirement of constant development.The pursuit of freedom,novel and beautiful architecture form has become the main trend in the development of the space structure today.The expressiveness which is free and flexible and the visual effect of rich aesthetic feeling of free-form surface structure become the frontiers of space structure research.For many free-form surface structures,however,the initial structure has an irregular shape and the span is large.Therefore,large displacement problem exists which requires geometric nonlinearity study.According to current situation of the study,this paper has carried out the following several aspects work:1.Create the initial structure model which can meet the need of architectural designFor the current development trend of building,we need to construct more and more rich boundary and free surface structure.Based on the B-spline curve calculation theory deduction from simple to complicated,the parametric cycle(2m-1)times the generation method of b-spline curve is constructed which is usd to create the B-spline curve boundary of free surface of the initial model.On the basis of B-spline curve calculation method,B-spline curved surface generation method is constructed which is usd to create the free surface of the initial structure.Through adjusting the key control points on the curved surface,the structure of the initial configuration can be convenient to adjust.Delaunay triangular grid technology is used to divide the surface which can provide generating smooth uniform grid.In this case,we can get the structures which meet the requirements of initial structure model of free-form surface.2.The geometric nonlinear finite element method for free-form surface structure is establishedIn practical engineering,the strain of some free curved surface structure with a certain load is very small,but the rigid body displacement is large.At this time,the balance condition should not be set up in front of the deformation on the initial configuration which should truthfully base on the real configuration after deformation in order to consider the effect of deformation on the balance.In this case,the original Cauchy strain expression is no longer applicable on the basis of the small deformation.It is necessary to define new strain expression which contains the quadratic term of displacement expression.In this paper,the explicit form of geometric nonlinear stiffness matrix is derived and the finite element program for free-form surface structure was compiled which considers the geometric nonlinear.3.The geometric nonlinear sensitivity of strain energy is derivedIn order to adjust and optimize the initial structure,this paper adopts the structure strain energy as the optimization of the evaluation index which can reflect the overall mechanical properties of the structure.The element stiffness matrix is derived for the key points of differential which is used to compile the calculation program of the sensitivity of strain energy and strain energy considering geometric nonlinearity of structure.4.A structural morphogenesis method is establishedIn this paper which based on the idea of structure optimization design,the B-spline curve surface function is used to establish the initial structure model.Delaunay triangulation segmentation is used to divide structure.The strain energy of the structure is calculated by the geometric nonlinear finite element program.Setting the minimum strain energy as the optimization target,the key point of the vertical surface structure can be adjusted according to the sensitivity of strain erengy.On the base of the above,the beautiful free-form surface structure shape with reasonable stress can be created step by step.5.The specific free-form surface examples are calculated and analyzedThe structural morphogenesis technique for free-form surface structures considering geometric nonlinear is used to calculate and analysis free-form surface examples with different internal and external boundary.The evolution process and mechanical properties of free-form surface structures are analyzed.The morphological changes are summarized during the process of free-form surface structure optimization.The characteristics of the mechanical properties of the free-form surface structure optimization are summarized.Based on FORTRAN language,structural morphogenesis creation program is compiled.Through concrete examples of optimization calculation,the mechanical properties of the free-form surface structure optimization are calculated and analyzed which validate the validity and practicability of the method.