Modified and Trefftz unsymmetric finite element models

Xie, Qiang; Sze, K. Y.; Zhou, Yexin

doi:10.1007/s10999-014-9289-3

Cited by 29 publications

(58 citation statements)

References 32 publications

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“…The normalized deflections at point A and the results of stresses at point B are given in Tables IV and V, respectively, and the results of deflections at points a 1 , a 2 , a 3 , and a 4 in selected mesh divisions under loadingP are also given in Table VI. From Tables IV and V, it can be seen that exact displacements and stresses under pure bending state can be obtained by element TH8 (ˇD0.01 and 0.0001) [46] and the new element US-ATFH8, no matter how meshes are distorted, and no matter whether the four corner nodes of the interface are Table VI. The results of deflections at points a 1 , a 2 , a 3 , and a 4 under loadP (Figure 4).…”

Section: Meshmentioning

confidence: 99%

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An unsymmetric 8‐node hexahedral element with high distortion tolerance

Zhou

Cen

Huang

et al. 2016

Numerical Meth Engineering

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SUMMARYAmong all 3D 8-node hexahedral solid elements in current finite element library, the 'best' one can produce good results for bending problems using coarse regular meshes. However, once the mesh is distorted, the accuracy will drop dramatically. And how to solve this problem is still a challenge that remains outstanding. This paper develops an 8-node, 24-DOF (three conventional DOFs per node) hexahedral element based on the virtual work principle, in which two different sets of displacement fields are employed simultaneously to formulate an unsymmetric element stiffness matrix. The first set simply utilizes the formulations of the traditional 8-node tri-linear isoparametric element, while the second set mainly employs the analytical trial functions in terms of 3D oblique coordinates (R, S, T). The resulting element, denoted by US-ATFH8, contains no adjustable factor, and can be used for both isotropic and anisotropic cases. Numerical examples show it can strictly pass both the first-order (constant stress/strain) patch test and the second-order patch test for pure bending, remove the volume locking, and provide the

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Section: Meshmentioning

confidence: 99%

“…From Tables 4 and 5, it can be seen that exact displacements and stresses under pure bending state can be obtained by element TH8 ( =0.01 and 0.0001) [46] and the new element US-ATFH8, no matter how meshes are distorted, and no matter whether the four corner nodes of the interface are coplanar or not.…”

Section: Cheung and Chen Beam Tests [17] (Figure 4)mentioning

confidence: 99%

An unsymmetric 8‐node hexahedral element with high distortion tolerance

Zhou

Cen

Huang

et al. 2016

Numerical Meth Engineering

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“…Recently, Shang and Ouyang [1] proposed a simple and robust 4-node 12-DOF quadrilateral membrane element US-Q4 for the classical elastic problems based on the unsymmetric finite element method [42][43][44]. The unsymmetric FEM, which has been successfully applied to various applications in past years [45][46][47][48][49], employs different interpolations for the test and trial functions in the element formulation. Demonstrated by numerical tests [1], the element US-Q4 exhibits good numerical accuracy and resistance to mesh distortions, even when the element shape is severely distorted into concave quadrilateral or triangle.…”

Section: Introductionmentioning

confidence: 99%

A simple unsymmetric 4‐node 12‐DOF membrane element for the modified couple stress theory

Shang

Qian

Cen

et al. 2019

Numerical Meth Engineering

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SummaryIn this work, the recently proposed unsymmetric 4‐node 12‐DOF (degree‐of‐freedom) membrane element (Shang and Ouyang, Int J Numer Methods Eng 113(10): 1589‐1606, 2018), which has demonstrated excellent performance for the classical elastic problems, is further extended for the modified couple stress theory, to account for the size effect of materials. This is achieved via two formulation developments. Firstly, by using the penalty function method, the kinematic relations between the element's nodal drilling DOFs and the true physical rotations are enforced. Consequently, the continuity requirement for the modified couple stress theory is satisfied in weak sense, and the symmetric curvature test function can be easily derived from the gradients of the drilling DOFs. Secondly, the couple stress field that satisfies a priori the related equilibrium equations is adopted as the energy conjugate trial function to formulate the element for the modified couple stress theory. As demonstrated by a series of benchmark tests, the new element can efficiently capture the size‐dependent responses of materials and is robust to mesh distortions. Moreover, as the new element uses only three conventional DOFs per node, it can be readily incorporated into the standard finite element program framework and commonly available finite element programs.

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“…Solid Finite Element Model. As lower-order elements are normally more inclined in engineering analyses due to their low construction cost [14], the trilinear H8 element portrayed in Figure 1 is selected to model the bridge structure. e mapping between the global Cartesian coordinates (x, y, z) and the natural coordinates (ξ, η, ζ) is expressed as…”

Section: Refined Solid Vehicle-bridgementioning

confidence: 99%

Refined Vehicle‐Bridge Interaction Analysis Using Incompatible Solid Finite Element for Evaluating Stresses and Impact Factors

Xie

Han

Yuan

2020

Advances in Civil Engineering

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e vehicle-bridge interaction can induce bridge vibration and consequently fatigue, durability deterioration, local damage, and even collapse of bridge structure. In this paper, a solid vehicle-bridge interaction (VBI) analysis method is developed to provide refined analysis on the bridge responses including displacement and local stress under vehicle loads. e incompatible solid finite element (FE) is introduced to model the bridge, where the element shear locking is alleviated by incompatible displacement modes without sacrificing the computational efficiency. Benchmark example shows the incompatible solid element has superior computational efficiency compared to the conventional solid element. By virtue of the mass-spring-damper vehicle model, the interaction between vehicle and bridge is simulated with point-to-point contact assumption and the coupled dynamic equations are solved via nonlinear iteration. A case study on a simply supported T-girder bridge is conducted to validate the developed solid VBI analysis method and then the dynamic impact factor (DIF) of the bridge is evaluated based on the computed stress results and compared to code values. Results show that the solid VBI analysis method yields more accurate time-history bridge responses including displacement and stress under moving vehicles than the grillage method despite higher computational cost. Particularly, it can simulate realistic stress distribution and concentration along any concerned sections as well as in local components, which can provide detail information on the bridge behavior under dynamic loads. On the other hand, the DIF based on the computed stress result generally agrees well with the code values except for heavy vehicles where the stress-based DIF is slightly higher than the value in Chinese code while lower than that of AASHTO, suggesting the value specified by Chinese code may underestimate the DIF of heavy vehicles in certain circumstances to which more attention should be paid.

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Modified and Trefftz unsymmetric finite element models

Cited by 29 publications

References 32 publications

An unsymmetric 8‐node hexahedral element with high distortion tolerance

An unsymmetric 8‐node hexahedral element with high distortion tolerance

A simple unsymmetric 4‐node 12‐DOF membrane element for the modified couple stress theory

Refined Vehicle‐Bridge Interaction Analysis Using Incompatible Solid Finite Element for Evaluating Stresses and Impact Factors

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