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Enhanced patch test of finite element methods

Science China(Physics,Mechanics & Astronomy) 2006年第2期49卷 213-227页

作者： chen wanji State Key Laboratory for Structural Analysis of Industrial Equipment Dalian University of Technology Dalian 116023 China

Theoretically, the constant stress patch test is not rigorous. Also, either the patch test of non-zero constant shear for Mindlin plate problem or non-zero strain gradient curvature of the microstructures cannot be performed. To improve the theory of the patch test, in this paper, based on the variational principle with relaxed continuity requirement of nonconforming element for homogeneous differential equations, the author proposed the individual element condition for passing the patch test and the convergence condition of the element: besides passing the patch test, the element function should include the rigid body modes and constant strain modes and satisfy the weak continuity condition, and no extra zero energy modes occur. Moreover, the author further established a variational principle with relaxed continuity requirement of nonconforming element for inhomogene-ous differential equations, the enhanced patch test condition and the individual element condition. To assure the convergence of the element that should pass the enhanced patch test, the element function should include the rigid body modes and non-zero strain modes which satisfied the equilibrium equations, and no spurious zero energy modes occur and should satisfy new weak continuity condition. The theory of the enhanced patch test pro-posed in this paper can be applied to both homogeneous and inhomogeneous differential equations. Based on this theory, the patch test of the non-zero constant shear stress for Mindlin plate and the C0-1 patch test of the non-zero constant curvature for the couple stress/strain gradient theory were established.

关键词： variational principle individual element condition patch test enhanced patch test Mindlin plate element couple stress/strain gradient theory.

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Measurement of length-scale and solution of cantilever beam in couple stress elasto-plasticity

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Acta Mechanica Sinica 2009年第3期25卷 381-387页

作者： Bin Ji wanji chen Jie Zhao State Key Laboratory for Structural Analysis of Industrial Equipment Dalian University of Technology 116023 Dalian China Department of Aeronautics and Space Navigation Shenyang Institute of Aeronautical Engineering Daoyi South Street 37 110136 Shenyang Liaoning China

Owing to the absence of proper analytical solution of cantilever beams for couple stress/strain gradient elasto-plastic theory, experimental studies of the cantilever beam in the micro-scale are not suitable for the determination of material length-scale. Based on the couple stress elasto-plasticity, an analytical solution of thin cantilever beams is firstly presented, and the solution can be regarded as an extension of the elastic and rigid-plastic solutions of pure bending beam. A comparison with numerical results shows that the current analytical solution is reliable for the case of σ0 〈〈 H 〈〈 E, where σ0 is the initial yield strength, H is the hardening modulus and E is the elastic modulus. Fortunately, the above mentioned condition can be satisfied for many metal materials, and thus the solution can be used to determine the material length-scale of micro-structures in conjunction with the experiment of cantilever beams in the micro-scale.

关键词： Material length-scale Couple stress elasto-plasticity Analytical solution Cantilever beam

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A size-dependent composite laminated skew plate model based on a new modified couple stress theory

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Acta Mechanica Solida Sinica 2017年第1期30卷 75-86页

作者： Dan He Wanli Yang wanji chen Key Laboratory of Liaoning Province for Composite Structural Analysis of Aerocraft and Simulation Shenyang Aerospace University

In this study, a size-dependent composite laminated skew Mindlin plate model is proposed based on a new modified couple stress theory. This plate model can be viewed as a simplified couple stress theory in engineering mechanics. Governing equations and related boundary conditions are derived based on the principle of minimum potential energy. The Rayleigh–Ritz method is employed to obtain the numerical solutions of the center deflections of simply supported plates with different ply orientations. Numerical results show that the normalized center deflections obtained by the proposed model are always smaller than those obtained by the classical one, i.e. the present model can capture the scale effects of microstructures. Moreover, a phenomenon reveals that the ply orientation would make a significant influence on the magnitude of scale effects of composite laminated plates at micro scale. Additionally, the present model of thick skew plate can be degenerated to the model of Kirchhoff plate based on the modified couple stress theory by adopting the assumptions in Bernoulli–Euler beam and material isotropy.

关键词： Modified couple stress theory Composite laminated plates Scale effects Ply orientation Rayleigh-Ritz method

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Patch test function for axisymmetric element of conventional and couple stress theory

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Science China(Physics,Mechanics & Astronomy) 2009年第8期52卷 1257-1261页

作者： chen wanji ZHAO Jie WANG JinZhi JI Bian Institute for Structural Analysis of Aerocraft Shenyang Institute of Aeronautical EngineeringShenyang 110136China State Key Laboratory for Structural Analysis of Industrial Equipment Dalian University of TechnologyDalian 116023China College of Science Institute of Dalian NationalitiesDalian 116022China

The enhanced patch test proposed by chen W J(2006) can be used to assess the convergence of the problem with non-homogeneous differential *** on this theory,we establish the patch test function for axisymmetric elements of conventional and couple stress theories,and reach an important conclusion that the patch test function for axisymmetric elements cannot contain non-zero constant shear.

关键词： axisymmetric element non-homogeneous differential equations couple stress theory test function of patch test

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ON THE EQUIVALENCE OF THE WILSON ELEMENT AND THE GENERALIZED HYBRID ELEMENT

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Acta Mechanica Sinica 1990年第1期6卷 64-68页

作者： chen wanji, Dalian University of Technology 1. Dalian University of Technology Dalian China

In this paper the equivalence of the generalized hybrid element and the modified Wilson element, which is derived by the generalized hybrid method, is proved.

关键词： Wilson nonconforming element modified Wilson element generalized hybrid element equivalent

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C^0 and C^1 theories and test functions for FEM patch test in microstructures

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Science China(Physics,Mechanics & Astronomy) 2010年第6期53卷 1086-1093页

作者： chen wanji Institute for Structural Analysis of Aerocraft,Shenyang Aerospace University,Shenyang 110136,China 1. Institute for Structural Analysis of Aerocraft Shenyang Aerospace University Shenyang 110136 China

Among many theories and categories in microstructures,rotation-displacement used as "independent" or "dependent" variables,is a noticeable topic. In FEM,it is called C0 and C1 theory. The convergence criteria of finite elements for microstructures are less mature than those for the conventional thin plate bending problem. In this paper,the patch test functions for assessing convergence of the C0 and C1 finite elements in microstructures is established based on the enhanced patch test theory. The author has further explored the C0 and C1 finite element theories and investigated the difference and correlation between their finite element formulations. Newly proposed finite element theories for microstructures are as follows:(1) the displacement-rotation dependent C1 element that requires the element function satisfying both C0 and C1 continuity;(2) the displacement-rotation independent C0 element which requires new convergence criteria,such as non-zero constant shear stress patch test and zero constant shear stress patch test for approximating C1 element.

关键词： couple stress theory displacement-rotation dependent theory displacement-rotation independent theory finite element method for microstructures test function for patch test

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小儿健脾膏外治功能性再发性腹痛疗效观察

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中国现代应用药学 2019年第4期36卷 475-477页

作者：陈婉姬杨明华浙江省立同德医院杭州310012 浙江省中药研究所有限公司杭州310023

目的观察小儿健脾膏外治功能性再发性腹痛的疗效。方法将120例功能性再发性腹痛患儿分为2组(治疗组和对照组),各60例,治疗组穴位贴敷小儿健脾膏,对照组口服654-2片和双歧杆菌三联活菌散。比较2组腹痛缓解和消失情况。结果治疗组疗效优... 详细信息

目的观察小儿健脾膏外治功能性再发性腹痛的疗效。方法将120例功能性再发性腹痛患儿分为2组(治疗组和对照组),各60例,治疗组穴位贴敷小儿健脾膏,对照组口服654-2片和双歧杆菌三联活菌散。比较2组腹痛缓解和消失情况。结果治疗组疗效优于对照组,2组腹痛消失率、腹痛缓解和消失时间有显著性差异(P<0.05)。结论小儿健脾膏穴位贴敷治疗功能性再发性腹痛疗效肯定,操作简单方便,患儿依从性好。

关键词：小儿健脾膏功能性再发性腹痛穴位贴敷疗效观察

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胃复春片对功能性消化不良大鼠胃肠功能的影响

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中国现代应用药学 2019年第7期36卷 829-832页

作者：陈炜陈婉姬杨明华杭州胡庆余堂药业有限公司杭州310015 浙江省立同德医院杭州310012 浙江省中药研究所杭州310023

目的考察胃复春片对胃肠动力障碍的改善作用。方法建立功能性消化不良(functional dyspepsia,FD)大鼠模型;以FD大鼠体质量、进食量、饮水量、胃平滑肌电活动情况、胃液分泌量、胃蛋白酶活性、肝脏与脾脏质量、胃病理情况等考察胃复春的... 详细信息

目的考察胃复春片对胃肠动力障碍的改善作用。方法建立功能性消化不良(functional dyspepsia,FD)大鼠模型;以FD大鼠体质量、进食量、饮水量、胃平滑肌电活动情况、胃液分泌量、胃蛋白酶活性、肝脏与脾脏质量、胃病理情况等考察胃复春的药效。结果模型组FD大鼠胃平滑肌电活动明显紊乱,体质量、进食量、饮水量明显减少、胃蛋白酶活性明显降低;经胃复春治疗后,上述现象明显缓解,大鼠体质量、进食量、饮水量明显增加,胃蛋白酶活性明显升高。结论胃复春能改善FD大鼠的一般状况,对FD大鼠胃酸过多有抑制作用,能提高模型大鼠的胃蛋白酶活性。

关键词：胃复春功能性消化不良胃肠功能

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修正偶应力理论层合薄板自由振动模型及尺度效应

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大连理工大学学报 2013年第3期53卷 313-321页

作者：李莉陈万吉李小鹏大连理工大学工业装备结构分析国家重点实验室辽宁大连116024 中国医科大学基础医学院物理与生物物理教研室辽宁沈阳110001 沈阳航空航天大学辽宁省飞行器复合材料结构分析与仿真重点实验室辽宁沈阳110136

通过引入各向异性的细观尺度复合材料层合板的本构方程,将各向同性修正偶应力理论推广到各向异性,基于虚功原理首次建立了复合材料层合板新修正偶应力理论的自由振动模型.该理论包含不同的两个材料细观参数,偶应力曲率应变不对称.但是,... 详细信息

通过引入各向异性的细观尺度复合材料层合板的本构方程,将各向同性修正偶应力理论推广到各向异性,基于虚功原理首次建立了复合材料层合板新修正偶应力理论的自由振动模型.该理论包含不同的两个材料细观参数,偶应力曲率应变不对称.但是,用于各向同性材料与原修正偶应力理论等价,为了便于工程应用,建立了只含一个细观材料参数的偶应力层合薄板理论弯曲和振动的简化模型.算例表明建立的偶应力层合薄板模型能用于分析层合板的自由振动尺度效应.

关键词：修正偶应力理论各向异性本构方程尺度效应层合薄板自由振动

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复合材料厚梁精化锯齿理论及有限元分析

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固体力学学报 2014年第4期35卷 384-390页

作者：任晓辉陈万吉吴振沈阳航空航天大学辽宁省飞行器复合材料结构分析与仿真重点实验室沈阳110136

由于具有预先满足层间应力连续的优点,锯齿理论被广泛研究和应用.然而,至今锯齿理论仍然存在如下难题:基于锯齿理论构造单元时,需使用满足单元间C1连续的插值函数,难于构造多节点高阶单元,而且精度较低.如果这些问题不被重视和解决,应... 详细信息

由于具有预先满足层间应力连续的优点,锯齿理论被广泛研究和应用.然而,至今锯齿理论仍然存在如下难题:基于锯齿理论构造单元时,需使用满足单元间C1连续的插值函数,难于构造多节点高阶单元,而且精度较低.如果这些问题不被重视和解决,应用此类理论分析复合材料力学问题可能得出不恰当的结论.通过发展高精度的考虑横法向应变的C0型锯齿理论,论文将克服已有锯齿理论遇到的上述难题.基于发展的锯齿理论,构造三节点梁单元验证发展理论模型的性能.

关键词： C0型锯齿理论三节点梁单元横法向应变层合梁横向位移导数

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