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基于修正余能原理三维杂交应力元应力形式的选取
THE SELECTION OF STRESS FORM OF THREE-DIMENSIONAL HYBRID STRESS ELEMENT BASED ON THE PRINCIPLE OF MODIFIED RESIDUAL ENERGY
投稿时间:2017-12-26  修订日期:2018-03-15
DOI:
中文关键词:  三维应力函数  杂交应力元  三维有限元  混合模型  假设应力场
英文关键词:three dimensional stress function  hybrid stress element  three-dimensional finite element  hybrid model
基金项目:开放式PRMMCs损伤演化分析软件设计与研发
作者单位E-mail
罗华栋 昆明理工大学 CSHLHD@163.com 
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中文摘要:
      基于修正余能原理构造了三维杂交应力元,采用由完备多项式导出满足平衡方程和协调方程的Maxwell和Morera等17种应力分量表达式,将17种应力分量表达式应用到三维杂交应力元中,分析了各应力形式对三维实体均匀拉伸、3D梁弯曲和剪切等问题计算精度及数值稳定性的影响,并给出各应力形式的性能评价。在选出最好应力形式基础上,以3D梁弯曲和剪切为例研究该应力函数多项式项数对计算结果的影响。计算结果表明,麦克斯韦应力函数具有更广的适用范围;当应力函数多项式项数取52项时,计算结果就达到收敛。
英文摘要:
      A three-dimensional hybrid stress element is constructed based on the principle of modified complementary energy. There are 17 kinds of stress components, such as Maxwell and Morera, which can satisfy the equilibrium equation and the compatibility equation . Applying 17 stress component expressions to 3d hybrid stress element. The effects of various stress forms on the calculation accuracy and numerical stability of three-dimensional solid uniform stretching, 3D beam bending and shearing problems are analyzed, and the performance evaluation of each stress form is given. In the best form of stress on the basis of bending beams and shear to 3D as an example to study the influence of stress on the calculation results of the function of the number of polynomials. The calculation results show that the Maxwell stress function has a wider range of application. When the stress function is 52 when the number of polynomials, the calculation results can achieve convergence.
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