Research On Morphogenesis Method Of Framed Structures

Structural morphogenesis is a new research direction of the interdiscipline ofarchitecture and structural enginnering. Based on structural analysis, structuralmorphogenesis methods are a series of thoeries and methods to seek a variety ofgood architectural shape. This study can promote the development of thearchitectural and structural design. Framed structures have many types and a widerange of applications in engineering. Therefore, the research on framed structuralmorphogenesis method has important application value and is helpful to diversifythe architectural forms. Based on the structural optimization theories, this structuralmorphogenesis method is put forward for the shape, topology and sizingoptimizition of framed structures under architectural space constraints aiming tomaximize the structural stiffness. The method can be applied to the structuralmorphogenesis of various framed structures. This paper mainly focused out thefollowing tasks:1. The nodal adjustment method for framed structuresThe expressions of nodal strain energy sensitivity are derived from therelationship between strain energy and the nodal coordinates. Moreover, theexpressions of strain energy sensitivity of nodes under the spatial constraints weregotten. The shape morphogenesis method of framed structure, which took themaximization of structural stiffness as the design objective, was put forward throughgradual nodal adjustment after the analysis of the properties of nodal strain energysensitivity. In order to increase the efficiency of the method, the method foramending the direction of nodal shift was studied further and the shapemorphogenesis method of framed structure was improved. It was found that thenodal strain energy sensitivity tended to zero in the convergence stage, and then thecorresponding structures were less sensitive to the initial defect.2. topology morphogenesis method of framed strucutres combining shapeand topology optimizationTo evalue the contribution degree of each element in the whole structure toresisting loads, the elemental strain energy sensitivity for addition and eliminationwas defined and taken as the efficiency index for bearing loads. The topology andshape morphogenesis method of the framed structures including the nodaladjustment was put forward after the strategy study of elemental addition andelimination and the analysis of the properties of the elemental strain energysensitivity. This method realised the topology change through the direct eliminationof inefficient elements and addition of new elements near the highly efficient elements and the nodal position and structural shape were amended by the nodaladjustment during the topology change. The initial structure may be simple orcomplex because the elements may be added or eliminated in this method. After thestructural shape was fixed, the size optimization was introduced to make thismorphogenesis method integrate the shape, topology and size optimization. Thismethod can be used for the morphogenesis of all kinds of framed strucutres in planeor space.3. Architectural space constraints considered in this mehtodTo enhance the usefulness of this method, the architectural spatial constraintsfrom the architectural requirements were expressed by B-spline curves and surfaces,etc.,and were reflected in the strain energy sensitivity to make the structures derivedform this method meet the architectural requirements. In addtion, the architecturalspatial constraints were embodied by the intial strucutres which were set through thedifferent layout of rods according to the influence of the initial structure on finalstructure. Since the initial structure was the starting point of the structural evlotionand provided the basic posssible allowable space for the generation of new rods, theinitial strucutres had an important role on the realization of the architectural spatialconstraints. This paper perfected the program fuctions of the method in a variety ofspatial constraints for different application situations. This further enhanced thepracticality of the method, and also enriched the theory of structural morphology.4. Application in the plane and spatial structures for this methodIn order to discuss the applicability fo the method, a number of applicationexamples were carried out such as trusses, tree-like structures, bridges, etc. in theplane and spatial structures. Numerical examples demonstrated the wideapplicability and practicality of this method. The morphorgenesis of these structureswas about the different support condition, different initial structures, differentmorphorgenesis strategyies and different structural types. The changes of structuralshape and mechanical behaviors in the evolutionary process were investigated tosummarize the properties of the method and the inflence of the morphorgenesisstrategyies on the change of strucutral shape. The strucutral shape derived from themethod had the geometrical characters which transferred loads to supports mainlyby the axis force. These strucutral shapes often appeared beatiful arc shape and thiswas benificial for the realization of artistic intention of architechtural shape.Moreover, the structural forms derived from this method conformed to mechanicalconcepts, which could be provided for the education of structural mechanics andstructural design as reference.5. The summary of mechanical properties of the structures by this methodFrom the change of mechanical quantities in the numerial examples, thetopology and shape morphogenesis method of framed structures can make the structure evolve in the direction of the decline of strain energy and bending moment,and the finial structure would transfer loads with axis force. The nodal adjustmenthad great contribution to the improvement of structural mechanical behaviors. Bychecking stability of the structures in the evolutionary process, it was found that thenodal adjustment can not only improve the structural stiffness and ultimate load, butalso less influence by the initial nodal defect. This illustrated that the method takingstrain energy as the objective function can increase the structural rigidity and thestructure of ultimate load; Moreover, the structures derived by the method are lesssensitive to the initial defect. These mechanical quantities will be improvedsimaltinously in the optimization process.The proposed method was coded in Fortran language, and finite elementcommercial software ANSYS was used in the calculation of some structuralmechinical behaviors. In addtion, this paper got the program of the morphogenesisof framed strucutres.