For structures that only the predicted bounds of uncertainties are available,this study proposes a Bayesianmethod to logically evaluate the nonprobabilistic reliability of structures based on multi-ellipsoid convex mo...For structures that only the predicted bounds of uncertainties are available,this study proposes a Bayesianmethod to logically evaluate the nonprobabilistic reliability of structures based on multi-ellipsoid convex model and performance test data.According to the given interval ranges of uncertainties,we determine the initial characteristic parameters of a multi-ellipsoid convex set.Moreover,to update the plausibility of characteristic parameters,a Bayesian network for the information fusion of prior uncertainty knowledge and subsequent performance test data is constructed.Then,an updated multi-ellipsoid set with the maximum likelihood of the performance test data can be achieved.The credible non-probabilistic reliability index is calculated based on the Kriging-based surrogate model of the performance function.Several numerical examples are presented to validate the proposed Bayesian updating method.展开更多
Reliability of mechanical structures is an important issue in the engineering field,especially in the field of aerospace and other high-tech sophisticated fields.Up to now,reliability-based evaluation and optimization...Reliability of mechanical structures is an important issue in the engineering field,especially in the field of aerospace and other high-tech sophisticated fields.Up to now,reliability-based evaluation and optimization methods have been widely applied in the safety analysis and design of mechanical structures.Many advanced algorithms for significantly improving the calculation efficiency and accuracy of solutions have been developed and gained successful applications in real engineering problems.Recently,with the advantages of strong versatility and well global-searching ability,more and more attention has been paid to the intelligent algorithm of mechanical structure reliability optimization design.展开更多
Accurately controlling the nodal lines of vibrating structures with topology optimization is a highly challenging task.The major difficulties in this type of problem include a large number of design variables,the high...Accurately controlling the nodal lines of vibrating structures with topology optimization is a highly challenging task.The major difficulties in this type of problem include a large number of design variables,the highly nonlinear and multi-peak characteristics of iteration,and the changeable orders of eigenmodes.In this study,an effective material-field series-expansion(MFSE)-based topology optimization design strategy for precisely controlling nodal lines is proposed.Here,two typical optimization targets are established:(1)minimizing the difference between structural nodal lines and their desired positions,and(2)keeping the position of nodal lines within the specified range while optimizing certain dynamic performance.To solve this complex optimization problem,the structural topology of structures is first represented by a few design variables on the basis of the MFSE model.Then,the problems are effectively solved using a sequence Kriging-based optimization algorithm without requiring design sensitivity analysis.The proposed design strategy inherently circumvents various numerical difficulties and can effectively obtain the desired vibration modes and nodal lines.Numerical examples are provided to validate the proposed topology optimization models and the corresponding solution strategy.展开更多
This paper presents a new robust topology optimization framework for hinge-free compliant mechanisms with spatially varying material uncertainties,which are described using a non-probabilistic bounded field model.Boun...This paper presents a new robust topology optimization framework for hinge-free compliant mechanisms with spatially varying material uncertainties,which are described using a non-probabilistic bounded field model.Bounded field uncertainties are efficiently represented by a reduced set of uncertain-but-bouncled coeflficients on the basis of the series expansion method.Robust topology optimization of compliant mechanisms is then defined to minimize the variation in output displacement under constraints of the mean displacement and predefined material volume.The nest optimization problem is solved using a gradient-based optimization algorithm.Numerical examples are presented to illustrate the effectiveness of the proposed method for circumventing hinges in topology optimization of compliant mechanisms.展开更多
This paper presents a MATLAB implementation of the material-field series-expansion(MFSE)topology optimization method.The MFSE method uses a bounded material field with specified spatial correlation to represent the st...This paper presents a MATLAB implementation of the material-field series-expansion(MFSE)topology optimization method.The MFSE method uses a bounded material field with specified spatial correlation to represent the structural topology.With the series-expansion method for bounded fields,this material field is described with the characteristic base functions and the corresponding coefficients.Compared with the conventional density-based method,the MFSE method decouples the topological description and the finite element discretization,and greatly reduces the number of design variables after dimensionality reduction.Other features of this method include inherent control on structural topological complexity,crisp structural boundary description,mesh independence,and being free from the checkerboard pattern.With the focus on the implementation of the MFSE method,the present MATLAB code uses the maximum stiffness optimization problems solved with a gradientbased optimizer as examples.The MATLAB code consists of three parts,namely,the main program and two subroutines(one for aggregating the optimization constraints and the other about the method of moving asymptotes optimizer).The implementation of the code and its extensions to topology optimization problems with multiple load cases and passive elements are discussed in detail.The code is intended for researchers who are interested in this method and want to get started with it quickly.It can also be used as a basis for handling complex engineering optimization problems by combining the MFSE topology optimization method with non-gradient optimization algorithms without sensitivity information because only a few design variables are required to describe relatively complex structural topology and smooth structural boundaries using the MFSE method.展开更多
基金This work was supported financially by the National Key R&D Program of China(2017YFB0203604)the National Natural Science Foundation of China(11972104,11772077)the Liaoning Revitalization Talents Program(XLYC1807187).
文摘For structures that only the predicted bounds of uncertainties are available,this study proposes a Bayesianmethod to logically evaluate the nonprobabilistic reliability of structures based on multi-ellipsoid convex model and performance test data.According to the given interval ranges of uncertainties,we determine the initial characteristic parameters of a multi-ellipsoid convex set.Moreover,to update the plausibility of characteristic parameters,a Bayesian network for the information fusion of prior uncertainty knowledge and subsequent performance test data is constructed.Then,an updated multi-ellipsoid set with the maximum likelihood of the performance test data can be achieved.The credible non-probabilistic reliability index is calculated based on the Kriging-based surrogate model of the performance function.Several numerical examples are presented to validate the proposed Bayesian updating method.
基金This work has been supported by the Natural Science Foundation of Shaanxi Province(2019JM-377)the Fundamental Research Funds for the Central Universities(NWPU-310202006zy007).
文摘Reliability of mechanical structures is an important issue in the engineering field,especially in the field of aerospace and other high-tech sophisticated fields.Up to now,reliability-based evaluation and optimization methods have been widely applied in the safety analysis and design of mechanical structures.Many advanced algorithms for significantly improving the calculation efficiency and accuracy of solutions have been developed and gained successful applications in real engineering problems.Recently,with the advantages of strong versatility and well global-searching ability,more and more attention has been paid to the intelligent algorithm of mechanical structure reliability optimization design.
基金supported financially by the Guangdong Basic and Applied Basic Research Foundation,China(Grant No.2022A1515240059)the National Natural Science Foundation of China(Grant No.52275237)the Shenzhen Stability Support Key Program in Colleges and Universities of China(Grant No.GXWD20220817133329001).
文摘Accurately controlling the nodal lines of vibrating structures with topology optimization is a highly challenging task.The major difficulties in this type of problem include a large number of design variables,the highly nonlinear and multi-peak characteristics of iteration,and the changeable orders of eigenmodes.In this study,an effective material-field series-expansion(MFSE)-based topology optimization design strategy for precisely controlling nodal lines is proposed.Here,two typical optimization targets are established:(1)minimizing the difference between structural nodal lines and their desired positions,and(2)keeping the position of nodal lines within the specified range while optimizing certain dynamic performance.To solve this complex optimization problem,the structural topology of structures is first represented by a few design variables on the basis of the MFSE model.Then,the problems are effectively solved using a sequence Kriging-based optimization algorithm without requiring design sensitivity analysis.The proposed design strategy inherently circumvents various numerical difficulties and can effectively obtain the desired vibration modes and nodal lines.Numerical examples are provided to validate the proposed topology optimization models and the corresponding solution strategy.
基金the National Key R&D Program of China(Grant No.2017YFB0203604)the National Natural Science Foundation of China(Grant No.11472215).
文摘This paper presents a new robust topology optimization framework for hinge-free compliant mechanisms with spatially varying material uncertainties,which are described using a non-probabilistic bounded field model.Bounded field uncertainties are efficiently represented by a reduced set of uncertain-but-bouncled coeflficients on the basis of the series expansion method.Robust topology optimization of compliant mechanisms is then defined to minimize the variation in output displacement under constraints of the mean displacement and predefined material volume.The nest optimization problem is solved using a gradient-based optimization algorithm.Numerical examples are presented to illustrate the effectiveness of the proposed method for circumventing hinges in topology optimization of compliant mechanisms.
基金The authors acknowledge the support of the National Key R&D Program of China(Grant No.2017YFB0203604)the National Natural Science Foundation of China(Grant Nos.11902064 and 11772077)the Liaoning Revitalization Talents Program,China(Grant No.XLYC1807187).
文摘This paper presents a MATLAB implementation of the material-field series-expansion(MFSE)topology optimization method.The MFSE method uses a bounded material field with specified spatial correlation to represent the structural topology.With the series-expansion method for bounded fields,this material field is described with the characteristic base functions and the corresponding coefficients.Compared with the conventional density-based method,the MFSE method decouples the topological description and the finite element discretization,and greatly reduces the number of design variables after dimensionality reduction.Other features of this method include inherent control on structural topological complexity,crisp structural boundary description,mesh independence,and being free from the checkerboard pattern.With the focus on the implementation of the MFSE method,the present MATLAB code uses the maximum stiffness optimization problems solved with a gradientbased optimizer as examples.The MATLAB code consists of three parts,namely,the main program and two subroutines(one for aggregating the optimization constraints and the other about the method of moving asymptotes optimizer).The implementation of the code and its extensions to topology optimization problems with multiple load cases and passive elements are discussed in detail.The code is intended for researchers who are interested in this method and want to get started with it quickly.It can also be used as a basis for handling complex engineering optimization problems by combining the MFSE topology optimization method with non-gradient optimization algorithms without sensitivity information because only a few design variables are required to describe relatively complex structural topology and smooth structural boundaries using the MFSE method.
