Optimization And Control Method For Static Displacement In Structural Engineering Based On Projection Optimization Method

Parameter selection and calculation of parameter modifications play a crucial role in structural optimization and control.These calculations heavily rely on sensitivity analysis.To improve the efficiency and accuracy of sensitivity calculations,scholars from both domestic and international backgrounds have proposed significant theories in sensitivity analysis.This paper introduces a first-order sensitivity calculation method for static displacement in structural engineering based on the Epsilon algorithm and the Neumann series algorithm.Additionally,a projection optimization method is presented for selecting appropriate parameters and calculating parameter modifications.Moreover,a multi-objective control method for static displacement and stiffener topology optimization method are proposed using the parameter optimization approach.The multi-objective control method is further extended to a multiobjective interval control method.The effectiveness of the multi-objective control method and the stiffener topology optimization method is demonstrated through examples of stiffener topology optimization and interval control.The main contributions of this paper are as follows:Firstly,the Epsilon algorithm is comprehensively introduced,including its solution,properties,and applications.Based on the Epsilon algorithm and the Neumann series algorithm,a method for computing first-order sensitivity of static displacement in structural engineering is proposed.The computational speed of this method is compared with other sensitivity solving methods,demonstrating its higher efficiency.The algorithm theoretically achieves rapid convergence to the target value and can be easily implemented through computer programming.After obtaining displacement sensitivities using the aforementioned method,the theoretical derivation of the projection optimization method for multi-objective control is presented.This method projects the column vectors of the displacement sensitivity matrix onto an h-dimensional subspace.The design parameters are then sorted in descending order based on the cosine values of the angles between the projection vectors and the corresponding sensitivity column vectors.In cases of equal cosine values,the sorting is based on the magnitudes of the projection vectors of the displacement sensitivity column vectors in the hdimensional subspace.Following parameter sorting,the required number of parameters is selected according to given criteria,and the corresponding optimal modification quantities are determined.This method is primarily applied to solve multi-parameter optimization problems.The 79-bar example demonstrates that the optimized parameter set obtained using the projection optimization method is closer to the target value compared to randomly selected parameter sets.This method exhibits high engineering application value based on the 79-bar example.The projection optimization method is extended and applied to stiffener topology optimization in plate-shell structures and uncertainty control optimization in truss structures.The method is iteratively employed multiple times to gradually approach the target value.During the optimization process,there exists a trade-off between calculation accuracy and efficiency.While reducing the step size of parameter modifications and the number of modified parameters can enhance the precision of optimization calculations,it may impact the convergence speed of displacement towards the target displacement.Hence,it is crucial to make a reasonable selection of the number of modified parameters and the step size of modifications.