Study On Efficient Algorithms For Static/Dynamic Reliability Analysis And Reliability-Based Design Optimization Of Structures

There exist various kinds of uncertainties in practical engineering structures,e.g.,material properties,geometric dimensions,manufacturing process and environmental loads,etc.These uncertainties exert large influence on the mechanical behavior and service performance of engineering structures directly.With the increasing demand for construction of large-scale and complex engineering structures,the reliability requirements of structures are also increased.Uncertainty quantification and propagation considering various uncertainties possesses academic and theoretical significance as well as engineering application value to structural reliability analysis and reliability-based design optimization.Reliability-based design optimization needs to conduct reliability analysis for many times,and the efficiency of reliability analysis will greatly restrict reliability-based design optimization.Therefore,it is urgent to develop efficient algorithms for structural reliability analysis and reliability-based design optimization.During the developing of structural reliability analysis and reliability-based design optimization,some urgent and important issues for the researchers are presented.When the performance function is highly nonlinear,the first order reliability method for reliability analysis exhibits non-convergence.Though single-loop approach exhibits higher efficiency than both double-loop approach and decoupled approach for solving reliability-based design optimization problems,single-loop approach suffers from the non-convergence difficulty during the most probable point(also termed as design point)searching process for reliability-based design optimization problem with highly nonlinear performance function.Furthermore,some performance functions for engineering structures are fairly complicated,e.g.,disjoint failure domains,discontinuous structural responses and multiple design points.The existing methods are difficult to address static and dynamic reliability assessment for structures with the above complicated performance functions in a unified framework.Moreover,there is also a lack of an efficient and unified framework for static and dynamic reliability-based design optimization problems with complicated performance functions(i.e.,multiple design points).Therefore,this dissertation aims to deeply study the above critical issues,and develop efficient methods for static and dynamic structural reliability assessment and reliability-based design optimization to serve the practical engineering.The main contents are presented as follows:(1)Based on the chaos control idea of discrete system,an accelerated stability transformation method is proposed to stabilize the unstable fixed points of nonlinear mapping functions,and then this method is utilized to conduct structural reliability analysis.For each step of iteration of the nonlinear mapping function,the accelerated stability transformation method adopts the stability transformation method twice to control the step size in the oscillation direction,and relaxes the step size of the direction normal to the oscillation direction and thus reduces computational efforts of chaos control remarkably.Numerical examples demonstrate that the proposed accelerated stability transformation method is more efficient and accurate than stability transformation method for stabilizing the unstable fixedpoints embedded in chaotic attractor.The first-order reliability method for structural reliability analysis constitutes a typical nonlinear iterative mapping,and the accelerated stability transformation method can achieve the convergence control of the first-order reliability iterative algorithm.(2)A hybrid self-adjusted single-loop approach is proposed to attack reliability-based design optimization problems with highly nonlinear performance function,for which the single-loop approach usually generates numerical instability and non-convergence solutions.To reduce the evaluation numbers of performance function and objective function,this dissertation firstly establishes a new oscillating judgement criterion to precisely detect the oscillation of iterative points in standard normal space and a self-adjusted updating strategy for the control factor of modified chaos control method.Then,an adaptive modified chaos control method is developed to search for design point efficiently based on the oscillation of iterative points.Finally,by integrating the adaptive modified chaos control method into single-loop approach,a hybrid self-adjusted single-loop approach is proposed.Representative examples reveal that the proposed hybrid self-adjusted single-loop approach enables to achieve stable convergence and enhance the computational efficiency for reliability-based design optimization problems with highly nonlinear performance function.(3)Based on the direct probability integral method for nonlinear stochastic dynamics analysis,an accurate,efficient and unified framework is developed to perform static and dynamic reliability assessment for structures with three kinds of challenging complicated performance functions,i.e.,disjoint failure domains,discontinuous structural responses and multiple design points.The direct probability integral method is competent to decouple the computation of structural physical equation and probability density integral equation,which is solved efficiently by adopting the partition of probability space and the smoothing of Dirac delta function.By combining the structural performance function with the probability density integral equation,the probability density functions of static and dynamic responses of structures with complicated performance functions are calculated.For performance functions with disjoint failure domains or arch structure with discontinuous response(i.e.,snap-through behavior),the direct probability integral method is capable of computing the probability density functions of structural responses and addressing reliability assessment accurately and efficiently.For reliability analysis of structures with multiple design points,the direct probability integral method enables us to avoid the complex computational process of searching all multiple design points.Furthermore,by constructing an equivalent extremum mapping,the direct probability integral method enables to accurately and efficiently fulfill dynamic reliability assessment for the frame building with a tuned mass damper containing two design points.(4)By introducing the change of probability measure into the direct probability integral method,an efficient method is established to address static and dynamic reliability-based design optimization problems with multiple design points.To perform reliability analysis,the probability density integral equation is integrated among the failure domain,and Dirac delta function can be analytically integrated into the Heaviside function,which avoids the smoothing of Dirac delta function for the direct probability integral method.The sensitivity of probabilistic constraint with respect to random design variable is calculated efficiently.by virtue of direct probability integral method and change of probability measure.It is shown that the established method can avoid the complex process of searching all design points in each optimization iterative process.Numerical examples validate the efficacy and versatility of the the direct probability integral method for addressing static/dynamic reliability-based design optimization problems with multiple design points.For dynamic reliability-based design optimization of the frame building with a tuned mass damper containing two design points under the random earthquake excitation,the established method enables to obtain a satisfactory optimization design,and the means of structural stiffnesses increase with the threshold of failure probability decrease.