| As along the development of technology, structural optimization has been an important branch of solid mechanics nowadays which is widely applied in many engineering fields, such as aerospace, mechanical manufacturing, vehicle and so on.Generally, there are always large-scale, high-order and nonlinear problems in the optimization actual structures which cost lots of time to analyze. Whether we can solve these problems except depending on constructing the reasonable mathematic model, choosing an available optimization method is also a key point. As a kind of most effective and popular sequential approximate programming, sequential linear programming (SLP) has been widely used in universal optimization software and structural optimization field. The main idea of SLP is transforming the nonlinear problems into linear ones by Taylor expansion. By means of solving the linear problems parelly, one can finally obtain the optimum solution of the original problem. However, traditional SLP method is restricted by the scales of problem so that it converges slowly. For solving the large-scale structural optimization problems, it is necessary to research an improved SLP method in order to enhance the convergence, stability and validity of original SLP. The research will be very meaningful and valuable in the engineering application.In practical engineering problems, the elastic mechanism with rigid modes accounts for a large proportion in mechanical structure. The movement of acceleration and deceleration will cause the load swing, resulting that the load is difficult to replace. Particularly in the system of flexible mechanical structure such as aircraft, large scale hoisting machinery and flexible robots, when the step input signal role under control, the system are coupling between rigid body motion and elastic motion, which is due to the elastic stiffness in the event of body movement transforming to elastic deformation and producing residual vibration, resulting that the entire system is difficult to pinpoint. Commonly, we use input-shaping to suppress residual vibration of elastic bodies on purpose, which is reasonable and well-planned to make use of the time-delay dynamics of elastic bodies. The dynamical behavior of PD combined with input-shaping control system, subject to step inputs, is investigated. The actuator efforts and energy usage of PD combined with input-shaping control system are described in general formula. Given the condition of the same feedback as PD, the PD combined with input shaping control minimizes actuator effort, saves energy, and speeds system response.The main work of this paper is presented followed:1. First of all the paper reviews the basic theory and the optimization process of SLP. Then it studies the moving limit concept of constraint in feasibility space to improve the convergence of SLP through sequence linear programming method. According to the size of move limit, it is designed to control the convergence of SLP. Numerical examples are verified the affective of move limit which is the foundation of the theory in next chapter.2. In order to overcome the approximate accuracy of SLP, we improves SLP algorithm affected by move limit, based on linear error and proposed trust region. At the iteration, the error between approximate model and true model is evaluated by approximately linear concept. Along with the linearly searching, the approximate accuracy is enhanced greatly, resulting in the size of move limit in the design space broadened and the accuracy improved naturally. Additionally, step size is adaptively adjusted, which can be used to choose whether accept the move limit, therefore the convergence process is speeded up. This algorithm is simple with strong convergence and robust.3. In this paper, it is proposed an improved SLP method (IP-TR-SLP), which solves the linear optimization problems by interior-point method basing on the concept of trust region. Nowadays, interior-point method and simplex method are the two main ways to solve the linear optimization problems. Simple method moves alone the boundary to search the optimum solution, while the interior-point method searches along the central path. When the problems are large-scale, including many constraint conditions, the efficiency and convergence of interior-point method will be better than the simple method. Thereby the interior-point method is fitting for solving practical optimization problems. This paper focus on how to improve the efficiency of interior-point method, using complementary interval as a penalty function into the objective function. Meanwhile, one can restrict the distance between the new iterative point and current iterative point based on the trust region in each iteration to ensure the reliability of approximate models during the iteration. Although the computational cost in each iteration does not decrease, (IP-TR-SLP) method shortens the whole computational time during optimization and there is no necessary constraint the initial feasible point that (IP-TR-SLP) method will applied expanded to solve the practical optimization problems, especially in large scale cases.4. The proposed D-SLP and IP-TR-SLP algorithms are introduced to verify the size optimization problem of classical truss structure with displacement, stress, and frequency constraints. Through the calculation of 10-bar, 25-bar and 72-bar, it is showed that these two improved algorithms are feasible and the accuracy of the numerical examples is not lower than that of those existed references. The efficiency of these two methods are tested by 200-bar examples. The data optimization of results shows that, in the calculation of 10-bar and 25-bar, the efficiency of IP-TR-SLP is lower than that of D-SLP, however, for large-scale structure, IP-TR-SLP is superior to D-SLP. Although IP-TR-SLP algorithm spent much time at every iterative step, it do speed up the whole optimization process due to the adaptive adjustment of step size based on trust region, apparently in large-scale structure optimization. As a result, the solution field of SLP is broadened by these two algorithms applying in topology optimization.5. Based on researching the dynamical performances of the flexible mechanisms with a rigid mode, it is introduced time-delay in a control system and presented PD combined with input-shaping control for the mechanical structures. The dynamical behavior of PD combined with input-shaping control system, subject to step inputs, is investigated. The actuator efforts and energy usage of PD combined with input-shaping control system are described in general formula. Given the condition of the same feedback gains as the PD feedback control, the PD combined with input shaping control minimizes actuator effort by 56%, saves energy by 47%, and speeds up the system-response.At last, the paper summaries all the study and prospects for the whole thesis.
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