复合材料层合结构的可靠性设计方法及优化算法研究
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摘要
纤维增强复合材料(FRP)是一种高强度、低密度材料,具有很多其它材料所没有的优点或特点,广泛应用于航空、航天、造船和汽车等领域。对于纤维增强复合材料结构的研究,特别是对结构可靠性分析及可靠性优化设计的研究,是近年来备受关注的问题。现有的可靠性分析和可靠性优化研究主要考虑概率不确定因素对结构性能的影响,而忽略了非概率及混合不确定性因素的影响。同时,由于结构系统可靠性分析一般涉及到大量的失效模式以及失效模式相关性问题,且可靠性设计通常为多重优化问题,计算量巨大,因此只有建立合适的可靠性分析模型及优化求解方法,才能提高计算效率,有效地解决复杂结构可靠性优化设计问题,满足实际工程设计的需求。
针对以上问题,本文的主要研究内容和取得的成果如下:
(1)建立了混合不确定性可靠性分析模型和优化设计模型,研究了优化问题的求解策略,并将其用于复合材料可靠性优化设计。在工程实际中,不确定信息常常是以混合不确定的方式存在,既有随机不确定,又会有区间不确定。为使理论模型真实反映客观实际,避免人为假定的风险,就必须合理评价这些混合不确定因素对结构性能的影响。本文针对随机变量和区间变量共存情况下的混合不确定信息,建立了可靠性分析模型和优化设计模型。该模型采用可靠性逆分析方法直接进行可靠性约束的评价,计算效率高,且能够有效避免通常正向可靠性分析中易发生的迭代奇异性。同时,在寻优过程中,结合可靠度分析逆解法和序列优化环方法,将可靠性优化问题中的优化问题和可靠性分析进行解耦,将多重可靠性优化转化为序列优化环,从而提高了可靠性优化问题的计算效率,拓展了其解决实际复杂工程问题的能力。
(2)研究和分析了粒子群优化算法(PSO),对其收敛性能进行改进,并将其用于可靠性优化设计问题的求解。对于实际工程中的高度非线性、多局部极值、目标函数不可导等复杂问题,传统的梯度型优化算法常常存在函数求导困难或不能求导的问题,导致可靠性优化设计无法进行。本论文研究了具有较高计算效率的智能优化算法——粒子群优化算法,针对该算法在寻优过程中遇到的过早收敛和后期收敛能力不足,分别提出了两种不同的改进措施;并首次采用改进的粒子群优化算法分析了复合材料层合结构可靠性优化设计问题,通过算例,论证了粒子群优化算法用于可靠性优化设计问题的可行性。
(3)讨论了复杂系统可靠性优化设计问题求解方法。对于复杂系统可靠性优化设计问题,既要保证设计结果具有较好的计算精度,又要使得计算成本可行。本文建立了一种基于粒子群优化算法PSO和有限元法ANSYS相结合的可靠性优化求解方法。该方法同时具备粒子群优化算法和有限元的优点:采用ANSYS对复杂系统进行结构分析,保障了应力和变形计算的精度;利用改进的PSO进行可靠性优化计算,可以在保证全局收敛性的同时,提高可靠性优化问题的计算效率。作为应用实例,本文对纤维缠绕复合材料压力容器进行强度分析和可靠性优化设计,并得到对实际设计具有重要参考意义的结果。算例表明,PSO和ANSYS相结合的可靠性优化求解方法具有较强的实用性和通用性,对解决复杂结构的优化计算和可靠性优化设计具有很大的潜力。
By virtue of its excellent properties, such as the high specific strength and high specific modulus, the Fiber Reinforced Plastics (FRP) has been widely used as structural materials in aircraft, space, marine and automobile, etc. The study on the FRP structures, especially on the reliability analysis and reliability-based optimization design (RBOD) has become an important concern. Many achievements have been made in the reliability-based studies utilizing the probability theory, but little has been done considering the non-probability or the mixed uncertainty factors. On the other hand, since the reliability analysis of structures usually involves a large number of failure modes, and the reliability analysis itself involves the solution to an optimization problem, the RBOD is computationally very expensive in general. Therefore, it is necessary to establish a theoretical framework of RBOD which can incorporate different uncertainty sources, and to develop a corresponding optimization strategy which can effectively solve the RBOD problems.
Achievements in this paper are listed as follows:
(1) A reliability-based design model and the optimal strategy under the mixture of random and interval variables is established. The method proposed is then employed to solve the reliability-based optimization design of composite structures. In reliability-based design (RBD), uncertainties are usually treated stochastically, and the variables are assumed to follow certain probability distribution. However, in many practical engineering applications, distributions of some random variables may not be precisely known, the possible values of these variables are only known to lie within specified intervals. In such cases, the random and interval variables are mixed together. In this paper, we proposed a method for analyzing the structural reliability and undertaking RBD under the mixture of random and interval variables. A formulation of percentile performance (inverse reliability analysis technique) is presented to directly evaluate the reliability constraints. This technique can avoid singularity problems which may occur in solving a direct reliability model during the iterative reliability assessment procedure. And to alleviate the computational burden, a sequential sing-loop procedure is employed to replace the computationally expensive double-loop procedure. With the proposed method, we studied the reliability-based optimization design of composite structures under the mixed uncertainties.
(2) A new approach for the particle swarm optimization (PSO) is proposed to improve the convergence performance of the algorithm, and it is applied to the RBOD problems. To overcome the disadvantage of slow search speed and premature convergence in the basic PSO, two special mutation-interference operators are introduced. And the improved PSO method is then applied to the RBDO of laminated composites. Numerical examples show that the improved PSO has high convergence and good stability, and it is efficient in dealing with the probabilistic optimal design of composite structures.
(3) The method for the reliability-based optimal design of complex structures is studied. For solving the RBOD problem of complex structures, it is important to make the calculation cost feasible while ensuring the design results with good accuracy. The present paper proposed a method combing PSO and ANSYS to answer the requirement. In the proposed method, ANSYS is employed to accurately calculate the response of structures, and PSO is used to find the global optimum solution. As an illustration and application of the proposed method, the reliability-based optimum design of a composite pressure vessel is worked out. Numerical examples show that the method combing PSO and ANSYS has great potential in solving the reliability-based design problem of complex structures.
针对以上问题,本文的主要研究内容和取得的成果如下:
(1)建立了混合不确定性可靠性分析模型和优化设计模型,研究了优化问题的求解策略,并将其用于复合材料可靠性优化设计。在工程实际中,不确定信息常常是以混合不确定的方式存在,既有随机不确定,又会有区间不确定。为使理论模型真实反映客观实际,避免人为假定的风险,就必须合理评价这些混合不确定因素对结构性能的影响。本文针对随机变量和区间变量共存情况下的混合不确定信息,建立了可靠性分析模型和优化设计模型。该模型采用可靠性逆分析方法直接进行可靠性约束的评价,计算效率高,且能够有效避免通常正向可靠性分析中易发生的迭代奇异性。同时,在寻优过程中,结合可靠度分析逆解法和序列优化环方法,将可靠性优化问题中的优化问题和可靠性分析进行解耦,将多重可靠性优化转化为序列优化环,从而提高了可靠性优化问题的计算效率,拓展了其解决实际复杂工程问题的能力。
(2)研究和分析了粒子群优化算法(PSO),对其收敛性能进行改进,并将其用于可靠性优化设计问题的求解。对于实际工程中的高度非线性、多局部极值、目标函数不可导等复杂问题,传统的梯度型优化算法常常存在函数求导困难或不能求导的问题,导致可靠性优化设计无法进行。本论文研究了具有较高计算效率的智能优化算法——粒子群优化算法,针对该算法在寻优过程中遇到的过早收敛和后期收敛能力不足,分别提出了两种不同的改进措施;并首次采用改进的粒子群优化算法分析了复合材料层合结构可靠性优化设计问题,通过算例,论证了粒子群优化算法用于可靠性优化设计问题的可行性。
(3)讨论了复杂系统可靠性优化设计问题求解方法。对于复杂系统可靠性优化设计问题,既要保证设计结果具有较好的计算精度,又要使得计算成本可行。本文建立了一种基于粒子群优化算法PSO和有限元法ANSYS相结合的可靠性优化求解方法。该方法同时具备粒子群优化算法和有限元的优点:采用ANSYS对复杂系统进行结构分析,保障了应力和变形计算的精度;利用改进的PSO进行可靠性优化计算,可以在保证全局收敛性的同时,提高可靠性优化问题的计算效率。作为应用实例,本文对纤维缠绕复合材料压力容器进行强度分析和可靠性优化设计,并得到对实际设计具有重要参考意义的结果。算例表明,PSO和ANSYS相结合的可靠性优化求解方法具有较强的实用性和通用性,对解决复杂结构的优化计算和可靠性优化设计具有很大的潜力。
By virtue of its excellent properties, such as the high specific strength and high specific modulus, the Fiber Reinforced Plastics (FRP) has been widely used as structural materials in aircraft, space, marine and automobile, etc. The study on the FRP structures, especially on the reliability analysis and reliability-based optimization design (RBOD) has become an important concern. Many achievements have been made in the reliability-based studies utilizing the probability theory, but little has been done considering the non-probability or the mixed uncertainty factors. On the other hand, since the reliability analysis of structures usually involves a large number of failure modes, and the reliability analysis itself involves the solution to an optimization problem, the RBOD is computationally very expensive in general. Therefore, it is necessary to establish a theoretical framework of RBOD which can incorporate different uncertainty sources, and to develop a corresponding optimization strategy which can effectively solve the RBOD problems.
Achievements in this paper are listed as follows:
(1) A reliability-based design model and the optimal strategy under the mixture of random and interval variables is established. The method proposed is then employed to solve the reliability-based optimization design of composite structures. In reliability-based design (RBD), uncertainties are usually treated stochastically, and the variables are assumed to follow certain probability distribution. However, in many practical engineering applications, distributions of some random variables may not be precisely known, the possible values of these variables are only known to lie within specified intervals. In such cases, the random and interval variables are mixed together. In this paper, we proposed a method for analyzing the structural reliability and undertaking RBD under the mixture of random and interval variables. A formulation of percentile performance (inverse reliability analysis technique) is presented to directly evaluate the reliability constraints. This technique can avoid singularity problems which may occur in solving a direct reliability model during the iterative reliability assessment procedure. And to alleviate the computational burden, a sequential sing-loop procedure is employed to replace the computationally expensive double-loop procedure. With the proposed method, we studied the reliability-based optimization design of composite structures under the mixed uncertainties.
(2) A new approach for the particle swarm optimization (PSO) is proposed to improve the convergence performance of the algorithm, and it is applied to the RBOD problems. To overcome the disadvantage of slow search speed and premature convergence in the basic PSO, two special mutation-interference operators are introduced. And the improved PSO method is then applied to the RBDO of laminated composites. Numerical examples show that the improved PSO has high convergence and good stability, and it is efficient in dealing with the probabilistic optimal design of composite structures.
(3) The method for the reliability-based optimal design of complex structures is studied. For solving the RBOD problem of complex structures, it is important to make the calculation cost feasible while ensuring the design results with good accuracy. The present paper proposed a method combing PSO and ANSYS to answer the requirement. In the proposed method, ANSYS is employed to accurately calculate the response of structures, and PSO is used to find the global optimum solution. As an illustration and application of the proposed method, the reliability-based optimum design of a composite pressure vessel is worked out. Numerical examples show that the method combing PSO and ANSYS has great potential in solving the reliability-based design problem of complex structures.
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