Study On Morphogenesis Technique For The Free-curved Single-layer Reticulated Shells

Single layer reticulated shell structures have free-form and flexible appearanceand comparatively reasonable mechanical properties, can cover large space and canbe easily installed, which have made them widely applied in the field of spatialstructures. But most of the surfaces are conventional analytical surfaces (cylindrical,spherical, hyperbolic paraboloid, etc.), even if more free surfaces are created whichare just the results of architects’ pursuit of freedom. And Currently-used reticulatedshell structures are more sensitive to initial geometric imperfections, and beyond acertain span, the stiffness and bearing capacity cannot meet the designrequirements. The single-layer reticulated shell structure is a kind of“shape-resistant” structure. How to create the lightweight, free, flexible reticulatedshell structure with good and stable performance is the current problem to besolved. For design of building structure and morphology, both the sufficient rigidityand the stability of the structure should be ensured. The stiffness and stability ofmechanical properties can be evaluated by the structural strain energy and strainenergy sensitivity. The smaller the strain energy is, the greater the structural rigidity;the smaller the strain sensitivity is, the smaller the change of the stability of themechanical properties from the nodes’ deviation.The differential of element stiffness matrix to coordinates of the nodes wasderived and the differential of coordinate transformation matrix to coordinates of thenodes was derived, and the differential of structural strain energy to the coordinatesof the nodes was also derived; non-uniform rational B-splines basic principles wereintroduced to create the initial shape; a morphogenesis technique for single-layerreticulated shell structures was established, by using the finite element method tocalculate the strain energy sensitivity to coordinates of the nodes, based on thenature of the strain energy sensitivity,the technique adjusts the node coordinatevector, and finally makes the structure tend to reach a reasonable form of minimumstrain energy. Also morphology of structures in the different bearing constraints anddifferent loading conditions were regarded as examples to examine the evolution ofshapes and the variation of mechanical properties, and the characteristics of themethod were summed up at last.According to demand for architectural design stage, morphogenesis forstructures in different space conditions and the initial shapes was studied, andflexible light and reasonable shapes were created. Also reticulated shell withconventional surface (cylindrical, spherical, hyperbolic paraboloid) was corrected,and the sensitivity of the ultimate strength to initial defects was compared. Although the proposed method regards strain as the target operation quantity,not only the stiffness increases in the process of evolution of the structures, but theultimate bearing capacity has also been significantly improved. The evolution ofstrain sensitivity gradually reduces the convergence stage close to zero, reducing theimpact on the mechanical properties from the nodes’ deviation, and effectivelyimproves the sensitivity to initial geometric imperfections. This method can not onlyachieve a variety of free-form surfaces but also can improve the structure’smechanical rationality under the conditions of architectural intentions, which is ofgreat significance to determination of the structures’ morphology.