Cellular thin-shell structures are widely applied in ultralightweight designs due to their high bearing capacity and strength-to-weight ratio.In this paper,a full-scale isogeometric topology optimization(ITO)method ba...Cellular thin-shell structures are widely applied in ultralightweight designs due to their high bearing capacity and strength-to-weight ratio.In this paper,a full-scale isogeometric topology optimization(ITO)method based on Kirchhoff-Love shells for designing cellular tshin-shell structures with excellent damage tolerance ability is proposed.This method utilizes high-order continuous nonuniform rational B-splines(NURBS)as basis functions for Kirchhoff-Love shell elements.The geometric and analysis models of thin shells are unified by isogeometric analysis(IGA)to avoid geometric approximation error and improve computational accuracy.The topological configurations of thin-shell structures are described by constructing the effective density field on the controlmesh.Local volume constraints are imposed in the proximity of each control point to obtain bone-like cellular structures.To facilitate numerical implementation,the p-norm function is used to aggregate local volume constraints into an equivalent global constraint.Several numerical examples are provided to demonstrate the effectiveness of the proposed method.After simulation and comparative analysis,the results indicate that the cellular thin-shell structures optimized by the proposed method exhibit great load-carrying behavior and high damage robustness.展开更多
A frequency error estimation is presented for the isogeometric free vibration analysis of Kirchhoff–Love cylindrical shells using both quadratic and cubic basis functions.By analyzing the discrete isogeometric equati...A frequency error estimation is presented for the isogeometric free vibration analysis of Kirchhoff–Love cylindrical shells using both quadratic and cubic basis functions.By analyzing the discrete isogeometric equations with the aid of harmonic wave assumption,the frequency error measures are rationally derived for the quadratic and cubic formulations for Kirchhoff–Love cylindrical shells.In particular,the governing relationship of the continuum frequency for Kirchhoff–Love cylindrical shells is naturally embedded into the frequency error measures without the need of explicit frequency expressions,which usually are not trivial for the shell problems.In accordance with these theoretical findings,the 2nd and 4th orders of frequency accuracy are attained for the isogeometric schemes using quadratic and cubic basis functions,respectively.Numerical results not only thoroughly verify the theoretical convergence rates of frequency solutions,but also manifest an excellent magnitude match between numerical and theoretical frequency errors for the isogeometric free vibration analysis of Kirchhoff–Love cylindrical shells.展开更多
令 G 是一个简单连通图。 图 G 的 Kirchhoff 指标是图 G 中所有顶点对之间的电阻距离之和。 图 G 的电阻距离等效于将图 G 中的每条边替换为一个单位电阻后得到的电网络 N 中任意节点对之间的 有效电阻。 一个包含 n + 2 个多边形和 n ...令 G 是一个简单连通图。 图 G 的 Kirchhoff 指标是图 G 中所有顶点对之间的电阻距离之和。 图 G 的电阻距离等效于将图 G 中的每条边替换为一个单位电阻后得到的电网络 N 中任意节点对之间的 有效电阻。 一个包含 n + 2 个多边形和 n + 1 个四边形的链,使得其中每个四边形的两条平行边各 与一个多边形有一条公共边,这样的链被称为多边形链。 本文利用电网络的标准技术和 S, T -同分 异构体的 Kirchhoff 指标的比较结果,刻画了 Kirchhoff 指标达到最大的极值多边形链为线性多 边形链 Ln, Kirchhoff 指标达到最小的极值多边形链为螺旋多边形链 Dn。 此结果推广了杨玉军 等人以及张雷雷刻画的基于 Kirchhoff 指标的极值亚苯基链的结果。展开更多
At my school,we made donations to children in the flooded areas last week.All the teachers and students volunteered,so did I.Besides books,I donated schoolbags,clothes,toys and so on.I am willing giving①away these th...At my school,we made donations to children in the flooded areas last week.All the teachers and students volunteered,so did I.Besides books,I donated schoolbags,clothes,toys and so on.I am willing giving①away these things,because I feel it's my duty to help those in trouble.展开更多
This paper scrutinizes the differences in the conceptualization of love between Korean and American women.Grounded in an analysis of literary figures,Brett and Kim Ji-young,the study unravels the intricate interplay o...This paper scrutinizes the differences in the conceptualization of love between Korean and American women.Grounded in an analysis of literary figures,Brett and Kim Ji-young,the study unravels the intricate interplay of cultural,historical,and societal forces shaping these perspectives.The contrasting landscapes of the United States,driven by ideals of freedom and individualism,and Korea,entrenched in Confucian values and collectivism,serve as crucibles for forming women’s roles,self-perception,and societal expectations.The examination extends to communication styles,illuminating the directness of American expression versus Korea’s reliance on formalism.Through this exploration,the paper illustrates the profound impact of cultural contexts on the intricate tapestry of love,offering a nuanced understanding of divergent viewpoints within a global context.展开更多
基金supported by the National Key R&D Program of China(Grant Number 2020YFB1708300)China National Postdoctoral Program for Innovative Talents(Grant Number BX20220124)+1 种基金China Postdoctoral Science Foundation(Grant Number 2022M710055)the New Cornerstone Science Foundation through the XPLORER PRIZE,the Knowledge Innovation Program of Wuhan-Shuguang,the Young Top-Notch Talent Cultivation Program of Hubei Province and the Taihu Lake Innovation Fund for Future Technology(Grant Number HUST:2023-B-7).
文摘Cellular thin-shell structures are widely applied in ultralightweight designs due to their high bearing capacity and strength-to-weight ratio.In this paper,a full-scale isogeometric topology optimization(ITO)method based on Kirchhoff-Love shells for designing cellular tshin-shell structures with excellent damage tolerance ability is proposed.This method utilizes high-order continuous nonuniform rational B-splines(NURBS)as basis functions for Kirchhoff-Love shell elements.The geometric and analysis models of thin shells are unified by isogeometric analysis(IGA)to avoid geometric approximation error and improve computational accuracy.The topological configurations of thin-shell structures are described by constructing the effective density field on the controlmesh.Local volume constraints are imposed in the proximity of each control point to obtain bone-like cellular structures.To facilitate numerical implementation,the p-norm function is used to aggregate local volume constraints into an equivalent global constraint.Several numerical examples are provided to demonstrate the effectiveness of the proposed method.After simulation and comparative analysis,the results indicate that the cellular thin-shell structures optimized by the proposed method exhibit great load-carrying behavior and high damage robustness.
基金support of this work by the National Natural Science Foundation of China(Grant Nos.12072302,11772280)the Natural Science Foundation of Fujian Province of China(No.2021J02003)is gratefully acknowledged.
文摘A frequency error estimation is presented for the isogeometric free vibration analysis of Kirchhoff–Love cylindrical shells using both quadratic and cubic basis functions.By analyzing the discrete isogeometric equations with the aid of harmonic wave assumption,the frequency error measures are rationally derived for the quadratic and cubic formulations for Kirchhoff–Love cylindrical shells.In particular,the governing relationship of the continuum frequency for Kirchhoff–Love cylindrical shells is naturally embedded into the frequency error measures without the need of explicit frequency expressions,which usually are not trivial for the shell problems.In accordance with these theoretical findings,the 2nd and 4th orders of frequency accuracy are attained for the isogeometric schemes using quadratic and cubic basis functions,respectively.Numerical results not only thoroughly verify the theoretical convergence rates of frequency solutions,but also manifest an excellent magnitude match between numerical and theoretical frequency errors for the isogeometric free vibration analysis of Kirchhoff–Love cylindrical shells.
文摘At my school,we made donations to children in the flooded areas last week.All the teachers and students volunteered,so did I.Besides books,I donated schoolbags,clothes,toys and so on.I am willing giving①away these things,because I feel it's my duty to help those in trouble.
文摘This paper scrutinizes the differences in the conceptualization of love between Korean and American women.Grounded in an analysis of literary figures,Brett and Kim Ji-young,the study unravels the intricate interplay of cultural,historical,and societal forces shaping these perspectives.The contrasting landscapes of the United States,driven by ideals of freedom and individualism,and Korea,entrenched in Confucian values and collectivism,serve as crucibles for forming women’s roles,self-perception,and societal expectations.The examination extends to communication styles,illuminating the directness of American expression versus Korea’s reliance on formalism.Through this exploration,the paper illustrates the profound impact of cultural contexts on the intricate tapestry of love,offering a nuanced understanding of divergent viewpoints within a global context.
