Morphogenesis Of Branching Structures Based On The Strain Energy Sensitivity

Branching structures have a broad applying foreground in long-span spatialstructures because of their beautiful configurations, reasonable mechanical behaviorsand a wide range covering. However, most researches of branching structures focus ontheir static behaviors in the case of the topology has been determined, but not onthe morphology design. With the construction of more and more branching structures,how to create a beautiful and reasonable mechanical structure, which can assure thestructural stiffness and the stable performance as well, is the current problem to besolved. The work on a structure stores in the form of stain energy. The smaller the strainenergy is, the greater the structural rigidity; the smaller the strain sensitivity is, thesmaller the change of the stability of the mechanical properties from the initialimperfections. Therefore, using the strain energy as the objective function in the designof branching structures is feasible.Basic principles of Non-uniform B-Splines and curves interpolation wereintroduced to create the superstructure as the spatial constraints. Then the differential ofelement stiffness matrix to nodal coordinates was derived, as well as the differential ofcoordinate transformation matrix to coordinates of the nodes. Based on this, we can getthe differential of structural strain energy to the nodal coordinates, which is used as abasis for nodes moving. Sensitivity of strain energy of elements was also derived, whichis used as a basis for operation of elements. Finally, morphogenesis of branchingstructure based on the strain energy sensitivity was proposed. By calculating the strainenergy sensitivity, we can adjust the position of the nodes, together with the operation ofelements. Thus we get a rational branching structure reaches the minimum of the strainenergy, which subtains axial force chiefly. So we can optimize the cross-section size toobtain a branching structure with excellent perforance finally. Operating strategies werealso given.According to the three cases which may exist in structural design, branchingstructural morphogenesis in different initial conditions was studied. Reasonable andbeautiful branching structures were created. By mechanical analysis of the structures we get, the characteristics of this numerical morphogenesis method were summarized.Besides, different operating strategies were studied to design different structures, whichproved that the method we proposed can get various and rational branching structuresaccording to the design intent of designers.Although the proposed branching structural morphogenesis method regards strainenergy as the objective function, the structural stiffness, ultimate bearing capacity andstability have been significantly improved during evolution, and the load mode turns toaxial force bearing mainly. The sensitivity of strain energy gradually reduced in theevolutionary process, which means the impact on the mechanical properties from thenodes’ deviation reducing, and the sensitivity to initial geometric imperfectionsimproving effectively. All these provide available references for branching structuraldesign and construction.