该文基于相场法和自适应PHT(Polynomial splines over Hierarchical T-meshes)等几何薄壳理论,建立了自适应PHT等几何薄壳结构断裂问题相场模型。从能量和断裂力学的角度出发,推导了Kirchhoff-Love薄壳自适应等几何断裂相场模型的微分方...该文基于相场法和自适应PHT(Polynomial splines over Hierarchical T-meshes)等几何薄壳理论,建立了自适应PHT等几何薄壳结构断裂问题相场模型。从能量和断裂力学的角度出发,推导了Kirchhoff-Love薄壳自适应等几何断裂相场模型的微分方程,并采用自适应PHT样条基函数作为插值函数,对位移场和相场进行离散。一方面,Kirchhoff-Love薄壳理论不需要转动自由度,大大减小了计算规模;另一方面,PHT样条几何精确且满足Kirchhoff-Love薄壳理论C1的连续性,同时PHT样条不仅继承了NURBS样条的优点,还具有局部细分。最后,编写了相应程序,对比分析经典数值算例,讨论了该断裂相场模型的正确性和收敛性。展开更多
In this work,the Hierarchical Quadrature Element Method(HQEM)formulation of geometrically exact shells is proposed and applied for geometrically nonlinear analyses of both isotropic and laminated shells.The stress res...In this work,the Hierarchical Quadrature Element Method(HQEM)formulation of geometrically exact shells is proposed and applied for geometrically nonlinear analyses of both isotropic and laminated shells.The stress resultant formulation is developed within the HQEM framework,consequently significantly simplifying the computations of residual force and stiffness matrix.The present formulation inherently avoids shear and membrane locking,benefiting from its high-order approximation property.Furthermore,HQEM’s independent nodal distribution capability conveniently supports local p-refinement and flexibly facilitates mesh generation in various structural configurations through the combination of quadrilateral and triangular elements.Remarkably,in lateral buckling analysis,the HQEM outperforms the weak-form quadrilateral element(QEM)in accuracy with identical nodal degrees of freedom(three displacements and two rotations).Under high-load nonlinear response,the QEM exhibits a maximum relative deviation of approximately 9.5%from the reference,while the HQEM remains closely aligned with the benchmark results.In addition,for the cantilever beam under tip moment,HQEM produces virtually no out-of-plane deviation,compared to a slight deviation of 0.00001 with QEM,confirming its superior numerical reliability.In summary,the method demonstrates high accuracy,superior convergence,and robustness in handling large rotations and complex post-buckling behaviors across a series of benchmark problems.展开更多
The testing of large structures is limited by high costs and long cycles, making scaling methods an attractive solution. However, the scaling process of elastic rings introduces complexities in multi-parameter geometr...The testing of large structures is limited by high costs and long cycles, making scaling methods an attractive solution. However, the scaling process of elastic rings introduces complexities in multi-parameter geometric distortions, leading to a diminution in the predictive accuracy of the distorted similitude. To address this challenge, this study formulates a novel set of scaling laws, tailored to account for the intricate geometric distortions associated with elastic rings. The proposed scaling laws are formulated based on the intrinsic deformation characteristics of elastic rings, rather than the traditional systemic governing equations. Numerical and experimental cases are conducted to assess the efficacy and precision of the proposed scaling laws, and the obtained results are compared with those achieved by traditional methods. The outcomes demonstrate that the scaling laws put forth by this study significantly enhance the predictive capabilities for deformations of elastic rings.展开更多
针对传统双向进化结构优化(Bi-directional Evolutionary Structural Optimisation,BESO)的优化结果存在边界锯齿化,以及水平集方法(Level Set Method,LSM),尤其是参数化水平集方法(Parametric Level Set Method,PLSM),优化效率低、优...针对传统双向进化结构优化(Bi-directional Evolutionary Structural Optimisation,BESO)的优化结果存在边界锯齿化,以及水平集方法(Level Set Method,LSM),尤其是参数化水平集方法(Parametric Level Set Method,PLSM),优化效率低、优化过程不稳定的问题,本文提出一种Multiquadric(MQ)拟插值和BESO结合的参数化水平集方法。首先,借鉴传统BESO计算单元灵敏度;然后,利用MQ拟插值参数化水平集函数,隐式地确定平滑的结构拓扑;最后,采用二分法计算水平函数阈值,驱动体积分数值逐步达到目标值。数值实验结果表明:与传统BESO相比,该方法的优化结果有连续清晰边界;该方法不需要求解大规模线性方程组,计算效率高,稳定性强。所提方法继承了PLSM边界光滑和BESO计算效率高、稳定性强的优点,能够有效解决不同结构拓扑优化问题。展开更多
文摘该文基于相场法和自适应PHT(Polynomial splines over Hierarchical T-meshes)等几何薄壳理论,建立了自适应PHT等几何薄壳结构断裂问题相场模型。从能量和断裂力学的角度出发,推导了Kirchhoff-Love薄壳自适应等几何断裂相场模型的微分方程,并采用自适应PHT样条基函数作为插值函数,对位移场和相场进行离散。一方面,Kirchhoff-Love薄壳理论不需要转动自由度,大大减小了计算规模;另一方面,PHT样条几何精确且满足Kirchhoff-Love薄壳理论C1的连续性,同时PHT样条不仅继承了NURBS样条的优点,还具有局部细分。最后,编写了相应程序,对比分析经典数值算例,讨论了该断裂相场模型的正确性和收敛性。
基金supported by the National Natural Science Foundation of China(Grant Nos.12472194,12002018,11972004,11772031,11402015).
文摘In this work,the Hierarchical Quadrature Element Method(HQEM)formulation of geometrically exact shells is proposed and applied for geometrically nonlinear analyses of both isotropic and laminated shells.The stress resultant formulation is developed within the HQEM framework,consequently significantly simplifying the computations of residual force and stiffness matrix.The present formulation inherently avoids shear and membrane locking,benefiting from its high-order approximation property.Furthermore,HQEM’s independent nodal distribution capability conveniently supports local p-refinement and flexibly facilitates mesh generation in various structural configurations through the combination of quadrilateral and triangular elements.Remarkably,in lateral buckling analysis,the HQEM outperforms the weak-form quadrilateral element(QEM)in accuracy with identical nodal degrees of freedom(three displacements and two rotations).Under high-load nonlinear response,the QEM exhibits a maximum relative deviation of approximately 9.5%from the reference,while the HQEM remains closely aligned with the benchmark results.In addition,for the cantilever beam under tip moment,HQEM produces virtually no out-of-plane deviation,compared to a slight deviation of 0.00001 with QEM,confirming its superior numerical reliability.In summary,the method demonstrates high accuracy,superior convergence,and robustness in handling large rotations and complex post-buckling behaviors across a series of benchmark problems.
基金Project supported by the National Natural Science Foundation of China(Nos.52405095,12272089,and 92360305)the Guangdong Basic and Applied Basic Research Foundation of China(No.2023A1515110557)+4 种基金the Natural Science Foundation of Liaoning Province of China(No.2023-BSBA-102)the Open Fund of National Key Laboratory of Particle Transport and Separation Technology of China(No.WZKF-2024-6)the Open Project of Guangxi Key Laboratory of Automobile Components and Vehicle Technology of China(Nos.2024GKLACVTKF07 and 2024GKLACVTKF06)the Basic Research Projects of Liaoning Provincial Department of Education of China(No.JYTQN2023162)the Fundamental Research Funds for the Central Universities of China(No.N2403022)。
文摘The testing of large structures is limited by high costs and long cycles, making scaling methods an attractive solution. However, the scaling process of elastic rings introduces complexities in multi-parameter geometric distortions, leading to a diminution in the predictive accuracy of the distorted similitude. To address this challenge, this study formulates a novel set of scaling laws, tailored to account for the intricate geometric distortions associated with elastic rings. The proposed scaling laws are formulated based on the intrinsic deformation characteristics of elastic rings, rather than the traditional systemic governing equations. Numerical and experimental cases are conducted to assess the efficacy and precision of the proposed scaling laws, and the obtained results are compared with those achieved by traditional methods. The outcomes demonstrate that the scaling laws put forth by this study significantly enhance the predictive capabilities for deformations of elastic rings.
文摘针对传统双向进化结构优化(Bi-directional Evolutionary Structural Optimisation,BESO)的优化结果存在边界锯齿化,以及水平集方法(Level Set Method,LSM),尤其是参数化水平集方法(Parametric Level Set Method,PLSM),优化效率低、优化过程不稳定的问题,本文提出一种Multiquadric(MQ)拟插值和BESO结合的参数化水平集方法。首先,借鉴传统BESO计算单元灵敏度;然后,利用MQ拟插值参数化水平集函数,隐式地确定平滑的结构拓扑;最后,采用二分法计算水平函数阈值,驱动体积分数值逐步达到目标值。数值实验结果表明:与传统BESO相比,该方法的优化结果有连续清晰边界;该方法不需要求解大规模线性方程组,计算效率高,稳定性强。所提方法继承了PLSM边界光滑和BESO计算效率高、稳定性强的优点,能够有效解决不同结构拓扑优化问题。
