结构力流分析与传力效率评估研究
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摘要
为研究荷载在结构内部的传递机理,实现对结构传力效率的定量评估,以薄壳结构为研究对象,提出了结构力流分析方法和传力效率评估方法。基于现有结构力流分析方法,针对薄壳结构的几何形态及受力特点,以平面传力路径法为基础推导了空间传力路径计算公式,并引入弯曲应变能比来反映薄壳面外弯矩的影响,建立了适用于薄壳结构力流分析的改进传力路径法。在此基础上,综合考虑力流长度和传力形式两方面因素,提出了等效力流长度的概念,定义了无量纲化的结构传力效率系数,解决了薄壳结构传力效率难以定量分析的难题。通过对典型薄壳结构的力流分析与传力效率评估,验证了所提方法的适用性和有效性,分析了结构几何参数、荷载作用形式以及边界条件等因素对结构传力效率的影响。研究结果表明:改进的结构力流分析方法能够从整体上揭示结构的工作机理,增进了对结构工作性能的本质认识,有助于从整体上优化结构设计;基于传力效率系数的结构传力效率评估符合结构概念,是一种有效的结构评估手段。
This paper aims to study load transmission mechanism and evaluate transmission efficiency quantitatively. Taking shell structures as research objects, an analysis method for load flow and an evaluation method for force transmission efficiency were proposed. Based on the existing analysis methods for load flow and considering the geometric and mechanical characteristics of shell structures, an improved method for analyzing load path was proposed. The calculation formula for spatial load path was derived based on plane load path analysis. Moreover, the bending strain energy ratio was introduced to reflect out-of-plane bending moment. The concept of equivalent load flow length was proposed to consider the load flow length and the load transmission form synthetically. The force transmission efficiency factor, a dimensionless parameter, was defined to analyze shell structures quantitatively. The applicability and effectiveness of the proposed method was validated by typical shell structure examples. The effects of geometric parameters, load forms and boundary conditions on force transmission efficiency were also discussed. The results show that the improved load path method can reveal the overall working mechanism of structures and improve the understanding of load transmission mechanism. Moreover, it is conducive to integrated structural optimization design. The evaluation method for force transmission efficiency conforms to the structural concept and can work as an effective structural evaluation tool.
This paper aims to study load transmission mechanism and evaluate transmission efficiency quantitatively. Taking shell structures as research objects, an analysis method for load flow and an evaluation method for force transmission efficiency were proposed. Based on the existing analysis methods for load flow and considering the geometric and mechanical characteristics of shell structures, an improved method for analyzing load path was proposed. The calculation formula for spatial load path was derived based on plane load path analysis. Moreover, the bending strain energy ratio was introduced to reflect out-of-plane bending moment. The concept of equivalent load flow length was proposed to consider the load flow length and the load transmission form synthetically. The force transmission efficiency factor, a dimensionless parameter, was defined to analyze shell structures quantitatively. The applicability and effectiveness of the proposed method was validated by typical shell structure examples. The effects of geometric parameters, load forms and boundary conditions on force transmission efficiency were also discussed. The results show that the improved load path method can reveal the overall working mechanism of structures and improve the understanding of load transmission mechanism. Moreover, it is conducive to integrated structural optimization design. The evaluation method for force transmission efficiency conforms to the structural concept and can work as an effective structural evaluation tool.
引文
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[12] 櫻井俊彰,川上博史,阿部正俊,高橋邦弘. 構造物の荷重経路U*解析におけるFEM計算の高速化[J]. 日本機械学會論文集(A編),2007,73(733): No.07-7013.
[13] 吴勃英,王德明,丁效华,等.数值分析原理[M].北京:科学出版社,2003:294-303. (WU Boying, WANG Deming, DING Xiaohua, et al. Principles of numerical analysis[M].Beijing: Science Press, 2003: 294-303. (in Chinese))
[14] 武岳, 苏岩, 李清朋, 胡庆杰. 自由曲面薄壳结构数值逆吊找形方法研究[J]. 建筑结构学报, 2018, 39(3): 19-25. (WU Yue, SU Yan, LI Qingpeng, HU Qingjie. Study on numerical inverse hanging method for freeform shell structure[J]. Journal of Building Structures, 2018, 39(3):19-25. (in Chinese))
[15] GAJANAN S. Rehabilitation, renovation, and preservation of concrete and masonry structure[M]. Detroit: American Concrete Institute, 1985: 31-94.
[2] JI T. Concepts for designing stiffer structures[J]. The Structural Engineer, 2003, 81(21):36- 42.
[3] BAUD R V. Fillet profiles for constant stress[J]. Product Engineering, 1934, 5(4): 133-134.
[4] NEUBER H. Theory of notch stresses: principles for exact calculation of strength with reference to structural form and material[M]. Berlin:Springer, 1958: 116-188.
[5] BERANEK W J. Berekening van platen[D]. Delft, Holland:Delft University of Technology, 1976: 22-96.
[6] MARHADI K, VENKATARAMAN S. Comparison of quantitative and qualitative information provided by different structural load path definitions[J]. International Journal for Simulation and Multidisciplinary Design Optimization, 2009, 3(3): 384- 400.
[7] TOMASZ S, TOMASZ L. On the solution of the three forces problem and its application in optimal designing of a class of symmetric plane frameworks of least weight[J]. Structural and Multidisciplinary Optimization, 2010, 42(6): 835-853.
[8] KELLY D W, ELSLEY M. A procedure for determining load paths in elastic continua[J]. Engineering Computations, 1995, 12(5): 415- 424.
[9] KELLY D W, TOSH M W. Interpreting load paths and stress trajectories in elasticity[J]. Engineering Computations, 2000, 17(2): 117-135.
[10] KELLY D W, HSU P, ASUDULLAH M. Load paths and load flow in finite element analysis[J]. Engineering Computations, 2001, 18(1/2): 304-313.
[11] HARASAKI H, ARORA J S. New concepts of transferred and potential transferred forces in structures[J]. Computer Methods in Applied Mechanics and Engineering, 2001, 191(3): 385- 406.
[12] 櫻井俊彰,川上博史,阿部正俊,高橋邦弘. 構造物の荷重経路U*解析におけるFEM計算の高速化[J]. 日本機械学會論文集(A編),2007,73(733): No.07-7013.
[13] 吴勃英,王德明,丁效华,等.数值分析原理[M].北京:科学出版社,2003:294-303. (WU Boying, WANG Deming, DING Xiaohua, et al. Principles of numerical analysis[M].Beijing: Science Press, 2003: 294-303. (in Chinese))
[14] 武岳, 苏岩, 李清朋, 胡庆杰. 自由曲面薄壳结构数值逆吊找形方法研究[J]. 建筑结构学报, 2018, 39(3): 19-25. (WU Yue, SU Yan, LI Qingpeng, HU Qingjie. Study on numerical inverse hanging method for freeform shell structure[J]. Journal of Building Structures, 2018, 39(3):19-25. (in Chinese))
[15] GAJANAN S. Rehabilitation, renovation, and preservation of concrete and masonry structure[M]. Detroit: American Concrete Institute, 1985: 31-94.