Lower bound analysis of plastic limit and shakedown state of orthotropic materials
QIN Fang1, ZHANG Lele1, CHEN Min2, CHEN Geng3
1. School of Mechanical, Electronic and Control Engineering, Beijing Jiaotong University, Beijing 100044, China; 2. Department of Industrial Design, Xi'an Jiaotong-Liverpool University, Suzhou 215123, China; 3. Institute for Materials Applications in Mechanical Engineering, RWTH Aachen University, Aachen 52062, Germany
Abstract：The purpose of this study is to predict the plastic limit and the shakedown state of orthotropic materials and structures. The Hill yield criterion is used in Melan's theory with the finite element method and large scale nonlinear programing combined to form a model to predict the plastic limit and the shakedown state of complex 3D structures made from multi-orthotropic materials. Several numerical examples are given to verify the accuracy, universality and efficiency of this method. The applicability of using shakedown theory to plastic analyses is extended in this work. This method can be used to design and assess structures made from orthotropic composites in engineering practice .
[1] LE C V, NGUYEN P H, ASKES H, et al. A computational homogenization approach for limit analysis of heterogeneous materials[J]. International Journal for Numerical Methods in Engineering, 2017, 112(10):1381-1401. [2] PASTOR J, TURGEMAN S, BOEHLER J P. Solution of anisotropic plasticity problems by using associated isotropic problems[J]. International Journal of Plasticity, 1990, 6(2):143-168. [3] ZHANG Y G, LU M W. Computational limit analysis of anisotropic axisymmetric shells[J]. International Journal of Pressure Vessels and Piping, 1994, 58(3):283-287. [4] YU H S, SLOAN S W. Limit analysis of anisotropic soils using finite elements and linear programming[J]. Mechanics Research Communications, 1994, 21(6):545-554. [5] YU H S, SLOAN S W. Finite element limit analysis of reinforced soils[J]. Computers & Structures, 1997, 63(3):567-577. [6] CAPSONI A, CORRADI L, VENA P. Limit analysis of orthotropic structures based on Hill's yield condition[J]. International Journal of Solids and Structures, 2001, 38(22-23):3945-3963. [7] 李华祥, 刘应华, 冯西桥, 等. 正交各向异性结构塑性极限载荷的上限分析[J]. 清华大学学报(自然科学版), 2001, 41(8):71-74. LI H X, LIU Y H, FENG X Q, et al. Upper bound analysis of plastic limit loads on orthotropic structures[J]. Journal of Tsinghua University (Science and Technology), 2001, 41(8):71-74. (in Chinese) [8] LI H X. Kinematic shakedown analysis of anisotropic heterogeneous materials:A homogenization approach[J]. Journal of Applied Mechanics, 2012, 79(4):041016. [9] 张宏涛, 刘应华, 徐秉业. 正交各向异性结构的塑性极限与安定下限分析[J]. 工程力学, 2006, 23(1):11-16. ZHANG H T, LIU Y H, XU B Y. Lower bound limit and shakedown analysis of orthotropic structures[J]. Engineering Mechanics, 2006, 23(1):11-16. (in Chinese) [10] ZHANG H T, LIU Y H, XU B Y. Plastic limit analysis of ductile composite structures from micro- to macro-mechanical analysis[J]. Acta Mechanica Solida Sinica, 2009, 22(1):73-84. [11] MELAN E. Zur plastizität des räumlichen kontinuums[J]. Archive of Applied Mechanics, 1938, 9(2):116-126. [12] HILL R. A theory of the yielding and plastic flow of anisotropic metals[J]. Proceedings of the Royal Society A:Mathematical, Physical and Engineering Sciences, 1948, 193(1033):281-297. [13] CHEN S S, LIU Y H, CEN Z Z. Lower bound shakedown analysis by using the element free Galerkin method and non-linear programming[J]. Computer Methods in Applied Mechanics and Engineering, 2008, 197(45-48):3911-3921. [14] SIMON J W, WEICHERT D. Numerical lower bound shakedown analysis of engineering structures[J]. Computer Methods in Applied Mechanics and Engineering, 2011, 200(41-44):2828-2839. [15] CARVELLI V, CEN Z Z, LIU Y, et al. Shakedown analysis of defective pressure vessels by a kinematic approach[J]. Archive of Applied Mechanics, 1999, 69(9-10):751-764.
2018, Vol. 58 
