A Variational Principle and Applications for a Class of Specified Stress Problems

WANG Jialin; ZHANG Junbo; HE Lin; CHEN Zhuo

doi:10.21656/1000-0887.410173

Volume 42 Issue 4

Apr. 2021

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WANG Jialin, ZHANG Junbo, HE Lin, CHEN Zhuo. A Variational Principle and Applications for a Class of Specified Stress Problems[J]. Applied Mathematics and Mechanics, 2021, 42(4): 331-341. doi: 10.21656/1000-0887.410173

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A Variational Principle and Applications for a Class of Specified Stress Problems

doi: 10.21656/1000-0887.410173

School of Civil Engineering, Chongqing Jiaotong University, Chongqing 400074, P.R.China

Received Date: 2020-06-13
Rev Recd Date: 2020-08-12
Publish Date: 2021-04-01

Abstract

Abstract

To solve some problems in the finite element analysis with specified conditions for stresses or internal forces, the inelastic strain as an additional unknown to meet the specified stress condition was introduced. The elastic mechanics governing equations meeting the specified stress conditions were described under the small deformation assumption. The potential variational principle and the virtual work equation were established with the displacements and unknown inelastic strains as independent variables. Then a generalized variational principle with 4 types of independent variables of the displacement, the elastic strain, the unknown inelastic strain and the stress, was presented. Based on the variational principle, the specified axial forces and the required adjustment quantities were arranged in a dual form in the equations for truss and beam elements. The ordinary stress analysis was realized under the condition with known adjustment quantities, and the required adjustment quantities were obtained with specified axial force conditions. The effects of material stiffness and internal force of a structure were considered in the new method with the prestressing reinforcement simulation improved based on the equivalent load method or the real physical reinforcement method. The method applies to the optimization and adjustment of cable forces in related structures. Numerical simulations of displacement optimization and cable tension adjustment for a cablestayed structure demonstrate the feasibility and accuracy of the presented theory and algorithm.
- specified stress problem,
- variational principle,
- finite element,
- inelastic strain,
- prestressing tendon,
- cable

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References(31)

References

[1]	AALAMI B O. Structural modeling of posttensioned members[J]. Journal of Structural Engineering,2000,126(2): 157-162.
[2]	KENNETH W S. Simplified equivalent loads of prestressing[J]. Journal of Structural Engineering,1991,117(11): 3538-3542.
[3]	OH B H, JEON S J. Limitations and realistic application of equivalent load methods in pre-stressed concrete structures[J]. Magazine of Concrete Research,2002,54(3): 223-231.
[4]	张道明, 梁力, 尹新生, 等. 预应力内荷载的新计算方法: 直接内载法[J]. 工程力学, 2007,24(3): 103-109.(ZHANG Daoming, LIANG Li, YIN Xinsheng, et al. New approach to calculate prestressed internal load: direct internal load method[J]. Engineering Mechanics,2007,24(3): 103-109.(in Chinese))
[5]	熊欢, 李鹏辉, 李庆斌, 等. PCCP受载响应分析中三种预应力施加方法的比较研究[J]. 水力发电学报, 2010,29(6): 178-186.(XIONG Huan, LI Penghui, LI Qingbin, et al. Comparative study of three methods for the prestressing simulation in the analysis of load-bearing response of a PCCP[J]. Journal of Hydroelectric Engineering,2010,29(6): 178-186.(in Chinese))
[6]	袁明, 颜东煌. PC箱梁竖向预应力张拉锚固阶段应力损失研究[J]. 公路交通科技, 2010,27(10): 53-57.(YUAN Ming, YAN Donghuang. Study on vertical prestress loss of PC box girder during stretching and anchoring stage[J]. Journal of Highway and Transportation Research and Development,2010,27(10): 53-57.(in Chinese))
[7]	黄侨, 杨大伟, 李忠龙. 预应力混凝土梁桥的NURBS 预应力束模型研究[J]. 公路交通科技, 2007,27(1): 51-54.(HUANG Qiao, YANG Dawei, LI Zhonglong. NURBS strand model for prestressed concrete girder bridges[J]. Journal of Highway and Transportation Research and Development,2007,27(1): 51-54.(in Chinese))
[8]	NIHAL A, AMIN G. Prestressing with unbonded internal or external tendons: analysis and computer model[J]. Journal of Structural Engineering,2002,128(12): 1493-1501.
[9]	王家林, 陈山林. 非节点连接有限元及其在加筋结构中的应用[J]. 应用力学学报, 2010,27(2): 418-422.(WANG Jialin, CHEN Shanlin. Theroy of non-nodal connection finite element methods and its application in reinforced structures[J]. Chinese Journal of Applied Mechanics,2010,27(2): 418-422.(in Chinese))
[10]	ASHRAF A, FILIP C F. Finite-element model for pretensioned concrete Girders[J]. Journal of Structural Engineering,2010,136(4): 401-409.
[11]	MOREIRA L S, SOUSA J B M, PARENTE E. Nonlinear finite element simulation of unbonded prestressed concrete beams[J]. Engineering Structures,2018,170: 167-177.
[12]	李义强, 张彦兵, 杨丽. ANSYS中准确施加斜拉桥索力方法的研究[J]. 国防交通工程与技术, 2006,4(1): 23-25.(LI Yiqiang, ZHANG Yanbing, YANG Li. A study of the accurate exertion of cable forces of cable stayed bridges by ANSYS[J]. Traffic Engineering & Technology for National Defence,2006,4(1): 23-25.(in Chinese))
[13]	叶梅新, 韩衍群, 张敏. 基于ANSYS平台的斜拉桥调索方法研究[J]. 铁道学报, 2006,28(4): 128-131.(YE Meixin, HAN Yanqun, ZHANG Min. Research on adjusting cable forces of cable-stayed bridges based on ANSYS[J]. Journal of the China Railway Society,2006,28(4): 128-131.(in Chinese))
[14]	程进, 江见鲸, 肖汝诚, 等. ANSYS二次开发技术及在确定斜拉桥成桥初始恒载索力中的应用[J]. 公路交通科技, 2002,19(3): 50-52.(CHENG Jin, JIANG Jianjing, XIAO Rucheng, et al. ANSYS software and its application in determination of initial cable forces in cable-stayed bridges under dead loads[J]. Journal of Highway and Transportation Research and Development,2002,19(3): 50-52.(in Chinese))
[15]	叶梅新, 韩衍群, 张敏. ANSYS二次开发技术在确定斜拉桥初始恒载索力中的应用[J]. 铁道科学与工程学报, 2005,2(5): 56-59.(YE Meixin, HAN Yanqun, ZHANG Min. Development and application of ANSYS in long-span cable-stayed bridge[J]. Journal of Railway Science and Engineering,2005,2(5): 56-59.(in Chinese))
[16]	张杨永, 周云岗, 姜海西. 基于ANSYS的超大跨度斜拉桥的索力模拟[J]. 沈阳建筑大学学报(自然科学版), 2009,25(5): 909-913.(ZHANG Yangyong, ZHOU Yungang, JIANG Haixi. Cable force simulation for super long-span cable-stayed bridges based on ANSYS[J]. Journal of Shenyang Jianzhu University (Natural Science),2009,25(5): 909-913.(in Chinese))
[17]	梁鹏, 肖汝诚, 张雪松. 斜拉桥索力优化实用方法[J]. 同济大学学报(自然科学版), 2003,31(11): 1270-1274.(LIANG Peng, XIAO Rucheng, ZHANG Xuesong. Pratical method of optimized of cable tensions for cable-stayed bridges[J]. Journal of Tongji University(Natural Science Edition),2003,31(11): 1270-1274.(in Chinese))
[18]	张杨永, 吴万忠, 周云岗. 斜拉桥索力精确模拟的矩阵分析法[J]. 重庆交通大学学报(自然科学版), 2009,28(6): 979-981, 1078.(ZHANG Yangyong, WU Wanzhong, ZHOU Yungang. Matrix analysis method for precise simulation of cable force of cable-stayed bridge[J]. Journal of Chongqing Jiaotong University (Natural Science),2009,28(6): 979-981, 1078.(in Chinese))
[19]	王家林, 何琳. 一种含非弹性收缩量的预应力筋单元: CN201410116301.0[P]. 2014-06-18.(WANG Jialin, HE Lin. A prestressing tendon element with inelastic shrinkage: CN201410116301.0[P]. 2014-06-18.(in Chinese))
[20]	王家林, 曹珂瑞. 一种基于指定应力的斜拉桥成桥索力调整方法[J]. 公路交通科技, 2020,37(6): 18-25.(WANG Jialin, CAO Kerui. Cable force adjustment method of cable-stayed bridge in finished state based on specified stress[J]. Journal of Highway and Transportation Research and Development,2020,37(6): 18-25.(in Chinese))
[21]	LI G, YU D H, LI H N. Seismic response analysis of reinforced concrete frames using inelasticity-separated fiber beam-column model[J]. Earthquake Engineering & Structural Dynamics,2018,47(5): 1291-1308.
[22]	李钢, 余丁浩, 李宏男. 基于拟力法的纤维梁有限元非线性分析方法[J]. 建筑结构学报, 2016,37(9): 61-68.(LI Gang, YU Dinghao, LI Hongnan. Nonlinear fiber beam element analysis based on force analogy method[J]. Journal of Building Structures,2016,37(9): 61-68.(in Chinese))
[23]	李钢, 靳永强, 董志骞, 等. 基于混合近似法的纤维梁单元非线性求解方法[J]. 土木工程学报, 2019,52(6): 81-91.(LI Gang, JIN Yongqiang, DONG Zhiqian, et al. Nonlinear solution method for fiber beam element based on the hybrid approximations method[J]. China Civil Engineering Journal,2019,52(6): 81-91.(in Chinese))
[24]	LI G, YU D H. Efficient inelasticity-separated finite-element method for material nonlinearity analysis[J]. Journal of Engineering Mechanics,2018,144(4): 04018008.
[25]	田宗漱, 卞学鐄. 多变量变分原理与多变量有限元方法[M]. 北京: 科学出版社, 2011.(TIAN Zongshu, BIAN Xuehuang. Multivariable Variational Principles and Multivariable Finite Element Methods [M]. Beijing: Science Press, 2011.(in Chinese))
[26]	胡海昌. 论弹性体力学与受范性体力学中的一般变分原理[J]. 物理学报, 1954,10(3): 259-290.(HU Haichang. On some variational priciples in the theory of elasticity and the theory of plasticity[J]. Acta Physica Sinica,1954,10(3): 259-290.(in Chinese))
[27]	WASHIZU K. Variational Methods in Elasticity and Plasticity [M]. 3rd ed. Oxford: Pergamon Press, 1982.
[28]	钱伟长. 大位移非线性弹性理论的变分原理和广义变分原理[J]. 应用数学和力学, 1988,9(1): 1-11.(CHIEN Weizang. Variational principles and generalized variational principles for nonlinear elasticity with finite dispiacemant[J]. Applied Mathematics and Mechanics,1988,9(1): 1-11.(in Chinese))
[29]	付宝连. 有限变形非线性的变形能原理及功的互等定理与变分原理的关系[J]. 燕山大学学报, 2002,26(1): 4-6, 19.(FU Baolian. Relations between deformation energy theorem and reciprocal theorem and variational principles in non-linear elasticity with finite displacements[J]. Journal of Yanshan University,2002,26(1): 4-6, 19.(in Chinese))
[30]	付宝连. 有限位移理论线弹性力学二类和三类混合变量的变分原理及其应用[J]. 应用数学和力学, 2017,38(11): 1251-1268.(FU Baolian. Variational principles for dual and triple mixed variables of linear elasticity with finite displacements and the application[J]. Applied Mathematics and Mechanics,2017,38(11): 1251-1268.(in Chinese))
[31]	樊涛, 梁立孚, 周利剑. 几何非线性非保守系统弹性力学广义拟变分原理[J]. 大庆石油学院学报, 2007,31(1): 120-125.(FAN Tao, LIANG Lifu, ZHOU Lijian. Generalized quasi-variational principles in geometric nonlinear non-conservative elasticity[J]. Journal of Daqing Petroleum Institute,2007,31(1): 120-125.(in Chinese))