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This paper presents a node shift method to find the optimal distribution of nodes in single-layer reticulated shells. The optimization process searches for the minimum strain energy configuration and this leads to reduced sensitivity in initial imperfections. Strain energy sensitivity numbers are derived for free shift and restricted shift where nodes can move freely in the 3D space or have to move within a predefined surface respectively. Numerical examples demonstrate the efficiency of the proposed approach. It was found that optimized structures achieve higher ultimate load and are less sensitive to imperfections than the initial structure. The configuration of the final structure is closely related to factors like the initial structural configuration, spatial conditions, etc. Based on different initial conditions, architects can be provided with diverse reasonable structures. Furthermore, by amending the defined shapes and nodal distributions, it is possible to improve the mechanical behavior of the structures.

Branching structures are mechanically efficient in supporting large-span structures, such as free-form roofs. To support a roof with a specified geometry, we present a novel shape and topology optimization method to find the optimal branching structure in this paper. In the proposed method, the branching structure is modelled as a cablenet, while the reaction forces in z-direction from the roof are converted to the upward external loads at the branching structure. The force densities of the members are the design variables. The optimal branching structure can be obtained by minimizing one of the several types of objective functions, e.g., the sum of the strain energy, the sum of the absolute value of the internal axial forces, and the sum of the absolute value of the force densities, etc. The shape of the branching structure represented by the nodal coordinates is determined by solving the linear equilibrium equations in terms of force densities. The topology is optimized by removing the members with small axial forces and incorporating the closely spaced nodes. If the allowable stress is specified for the members, their cross-sectional areas can be directly calculated from the force densities and member lengths. Hence, it is very convenient to use force densities for simultaneously optimizing the cross-section, shape, and topology of a branching structure. Numerical examples show that this method can be easily applied to a 2D problem; however, for a 3D problem, the tolerances of the constraints on the reaction forces should be relaxed. It is also shown that considering the roof supports as variables is effective for finding an optimal shape of 3D branching structure supporting a free-form surface.

In this paper, 42.5 sulfate aluminate cement mixing pozzolan was used to prepare fast early strength concrete to reduce the application costs by the equivalent of cement, Pozzolan content, sand ratio, water-cement ratio investigated by orthogonal experiment method to seek meet with the strength requirements C30 concrete. Then the relationship between the concrete aggregate / cement-slurry ratio, dosage of water reducer and the slump, the strength were studied under the optimal concrete design.