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1 – 10 of over 20000Gives a bibliographical review of the finite element methods (FEMs) applied for the linear and nonlinear, static and dynamic analyses of basic structural elements from the…
Abstract
Gives a bibliographical review of the finite element methods (FEMs) applied for the linear and nonlinear, static and dynamic analyses of basic structural elements from the theoretical as well as practical points of view. The range of applications of FEMs in this area is wide and cannot be presented in a single paper; therefore aims to give the reader an encyclopaedic view on the subject. The bibliography at the end of the paper contains 2,025 references to papers, conference proceedings and theses/dissertations dealing with the analysis of beams, columns, rods, bars, cables, discs, blades, shafts, membranes, plates and shells that were published in 1992‐1995.
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Based on the recent advances of hybrid stress finite elements, a seriesof alternative stress assumptions for these elements are investigated.Several new element models are…
Abstract
Based on the recent advances of hybrid stress finite elements, a series of alternative stress assumptions for these elements are investigated. Several new element models are proposed by using different concepts for the stress interpolation. Under a unified formulation presented in this paper for Hellinger—Reissner principle based hybrid stress element models, the element series 5β‐family for plane stress and 18β‐family for three‐dimensional problems are discussed. The extra incompatible displacements sometimes also added are not introduced in this unified formulation. A number of popular benchmark elastic problems are examined for both two element families. In each family, the element model presented in this paper using normalized transformed higher order stress trials usually gives better predictions than the others.
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Hongxing Jia, Shizhu Tian, Shuangjiang Li, Weiyi Wu and Xinjiang Cai
Hybrid simulation, which is a general technique for obtaining the seismic response of an entire structure, is an improvement of the traditional seismic test technique. In order to…
Abstract
Purpose
Hybrid simulation, which is a general technique for obtaining the seismic response of an entire structure, is an improvement of the traditional seismic test technique. In order to improve the analysis accuracy of the numerical substructure in hybrid simulation, the purpose of this paper is to propose an innovative hybrid simulation technique. The technique combines the multi-scale finite element (MFE) analysis method and hybrid simulation method with the objective of achieving the balance between the accuracy and efficiency for the numerical substructure simulation.
Design/methodology/approach
To achieve this goal, a hybrid simulation system is established based on the MTS servo control system to develop a hybrid analysis model using an MFE model. Moreover, in order to verify the efficiency of the technique, the hybrid simulation of a three-storey benchmark structure is conducted. In this simulation, a ductile column—represented by a half-scale scale specimen—is selected as the experimental element, meanwhile the rest of the frame is modelled as microscopic and macroscopic elements in the Abaqus software simultaneously. Finally, to demonstrate the stability and accuracy of the proposed technique, the seismic response of the target structure obtained via hybrid simulation using the MFE model is compared with that of the numerical simulation.
Findings
First, the use of the hybrid simulation with the MFE model yields results similar to those obtained by the fine finite element (FE) model using solid elements without adding excessive computing burden, thus advancing the application of the hybrid simulation in large complex structures. Moreover, the proposed hybrid simulation is found to be more versatile in structural seismic analysis than other techniques. Second, the hybrid simulation system developed in this paper can perform hybrid simulation with the MFE model as well as handle the integration and coupling of the experimental elements with the numerical substructure, which consists of the macro- and micro-level elements. Third, conducting the hybrid simulation by applying earthquake motion to simulate seismic structural behaviour is feasible by using Abaqus to model the numerical substructure and harmonise the boundary connections between three different scale elements.
Research limitations/implications
In terms of the implementation of the hybrid simulation with the MFE model, this work is helpful to advance the hybrid simulation method in the structural experiment field. Nevertheless, there is still a need to refine and enhance the current technique, especially when the hybrid simulation is used in real complex engineering structures, having numerous micro-level elements. A large number of these elements may render the relevant hybrid simulations unattainable because the time consumed in the numeral calculations can become excessive, making the testing of the loading system almost difficult to run smoothly.
Practical implications
The MFE model is implemented in hybrid simulation, enabling to overcome the problems related to the testing accuracy caused by the numerical substructure simplifications using only macro-level elements.
Originality/value
This paper is the first to recognise the advantage of the MFE analysis method in hybrid simulation and propose an innovative hybrid simulation technique, combining the MFE analysis method with hybrid simulation method to strike a delicate balance between the accuracy and efficiency of the numerical substructure simulation in hybrid simulation. With the help of the coordinated analysis of FEs at different scales, not only the accuracy and reliability of the overall seismic analysis of the structure is improved, but the computational cost can be restrained to ensure the efficiency of hybrid simulation.
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Based on the orthogonal approach for hybrid element methods, refined three‐dimensional isoparametric hybrid hexahedral elements have been developed. The behaviour of the proposed…
Abstract
Based on the orthogonal approach for hybrid element methods, refined three‐dimensional isoparametric hybrid hexahedral elements have been developed. The behaviour of the proposed models are discussed in respect of coordinate invariance, spurious zero energy modes and the ability to pass the patch test. By adopting the orthogonality of strain energy, the element stiffness matrix can be decomposed into a series of stiffness matrices in which the implementational effectiveness can be improved. A number of examples is used to demonstrate the implementation efficiency, accuracy and distortion insensitivity of the proposed elements, and its capacity of handling nearly incompressible materials
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Qing Xie, Yucai Hu, Yexin Zhou and Wanshui Han
Poor bending response is a major shortcoming of lower-order elements due to excessive representation of shear stress/strain field. Advanced finite element (FE) formulations for…
Abstract
Purpose
Poor bending response is a major shortcoming of lower-order elements due to excessive representation of shear stress/strain field. Advanced finite element (FE) formulations for classical elasticity enhance the bending response by either nullifying or filtering some of the symmetric shear stress/strain modes. Nevertheless, the stress/strain field in Cosserat elasticity is asymmetric; consequently any attempt to nullify or filter the anti-symmetric shear stress/strain modes may lead to failure in the constant couple-stress patch test where the anti-symmetric shear stress/strain field is linear. This paper aims at enhancing the bending response of lower-order elements for Cosserat elasticity problems.
Design/methodology/approach
A four-node quadrilateral and an eight-node hexahedron are formulated by hybrid-stress approach. The symmetric stress is assumed as those of Pian and Sumihara and Pian and Tong. The anti-symmetric stress components are first assumed to be completely linear in order to pass the constant couple-stress patch test. The linear modes are then constrained with respect to the prescribed body-couple via the equilibrium conditions.
Findings
Numerical tests show that the hybrid elements can strictly pass the constant couple-stress patch test and are markedly more accurate than the conventional elements as well as the incompatible elements for bending problems in Cosserat elasticity.
Originality/value
This paper proposes a hybrid FE formulation to improve the bending response of four-node quadrilateral and eight-node hexahedral elements for Cosserat elasticity problems without compromising the constant couple-stress patch test.
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This paper gives a bibliographical review of the finite element methods (FEMs) applied for the linear and nonlinear, static and dynamic analyses of basic structural elements from…
Abstract
This paper gives a bibliographical review of the finite element methods (FEMs) applied for the linear and nonlinear, static and dynamic analyses of basic structural elements from the theoretical as well as practical points of view. The bibliography at the end of the paper contains more than 1330 references to papers, conference proceedings and theses/dissertations dealing with the analysis of beams, columns, rods, bars, cables, discs, blades, shafts, membranes, plates and shells that were published in 1999–2002.
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Song Cen, Cheng Jin Wu, Zhi Li, Yan Shang and Chenfeng Li
The purpose of this paper is to give a review on the newest developments of high-performance finite element methods (FEMs), and exhibit the recent contributions achieved by the…
Abstract
Purpose
The purpose of this paper is to give a review on the newest developments of high-performance finite element methods (FEMs), and exhibit the recent contributions achieved by the authors’ group, especially showing some breakthroughs against inherent difficulties existing in the traditional FEM for a long time.
Design/methodology/approach
Three kinds of new FEMs are emphasized and introduced, including the hybrid stress-function element method, the hybrid displacement-function element method for Mindlin–Reissner plate and the improved unsymmetric FEM. The distinguished feature of these three methods is that they all apply the fundamental analytical solutions of elasticity expressed in different coordinates as their trial functions.
Findings
The new FEMs show advantages from both analytical and numerical approaches. All the models exhibit outstanding capacity for resisting various severe mesh distortions, and even perform well when other models cannot work. Some difficulties in the history of FEM are also broken through, such as the limitations defined by MacNeal’s theorem and the edge-effect problems of Mindlin–Reissner plate.
Originality/value
These contributions possess high value for solving the difficulties in engineering computations, and promote the progress of FEM.
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A bibliographical review of the finite element methods (FEMs) applied for the linear and nonlinear, static and dynamic analyses of basic structural elements from the theoretical…
Abstract
A bibliographical review of the finite element methods (FEMs) applied for the linear and nonlinear, static and dynamic analyses of basic structural elements from the theoretical as well as practical points of view is given. The bibliography at the end of the paper contains 1,726 references to papers, conference proceedings and theses/dissertations dealing with the analysis of beams, columns, rods, bars, cables, discs, blades, shafts, membranes, plates and shells that were published in 1996‐1999.
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M. Baumann, K. Schweizerhof and S. Andrussow
A fully mixed hybrid 4‐node shell element for linear analyses ispresented and compared to the current state‐of‐the‐art.The specific improvements developed concern the stress…
Abstract
A fully mixed hybrid 4‐node shell element for linear analyses is presented and compared to the current state‐of‐the‐art. The specific improvements developed concern the stress assumptions for the transverse shear stresses in the in‐plane directions, such that the element is applicable for arbitrary element geometries without shear locking and satisfies the patch test exactly. Furthermore, in analogy to the membrane and bending part the shear part of the stiffness matrix can be formulated as a one‐point integrated constant part with a rank‐two update representing the linear parts. However, this efficient formulation leads to additional approximations concerning the geometry of arbitrarily curved elements. The latter aspect is discussed with some numerical examples, which demonstrate the capabilities of the developed element.
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This paper aims to develop a hybrid finite difference‐finite element method and apply it to solve the three‐dimensional energy equation in non‐isothermal fluid flow past over a…
Abstract
Purpose
This paper aims to develop a hybrid finite difference‐finite element method and apply it to solve the three‐dimensional energy equation in non‐isothermal fluid flow past over a tube.
Design/methodology/approach
To implement the hybrid scheme, the tube length is partitioned into uniform segments by choosing grid points along its length, and a plane perpendicular to the tube axis is drawn at each of the points. Subsequently, the Taylor‐Galerkin finite element technique is employed to discretize the energy equation in the planes; while the derivatives along the tube are discretized using the finite difference method.
Findings
To demonstrate the validity of the proposed numerical scheme, three‐dimensional test cases have been solved using the method. The variation of L2‐norm of the error with mesh refinement shows that the numerical solution converges to the exact solution with mesh refinement. Moreover, comparison of the computational time duration shows that the proposed method is approximately three times faster than the 3D finite element method. In the non‐isothermal fluid flow around a tube for Re=250 and Pr=0.7, the results show that the Nusselt number decreases with the increase in the tube length and, for the tube length greater than six times the tube diameter, the average Nusselt number converges to the value for the two‐dimensional case.
Originality/value
A hybrid finite difference‐finite element method has been developed and applied to solve the 3D transient energy equation for different test cases. The proposed method is faster, and computationally more efficient, compared with the 3D finite element method.
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