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Article
Publication date: 1 June 1997

Jaroslav Mackerle

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…

6041

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.

Details

Engineering Computations, vol. 14 no. 4
Type: Research Article
ISSN: 0264-4401

Keywords

Article
Publication date: 21 March 2019

Zhenhan Yao, Xiaoping Zheng, Han Yuan and Jinlong Feng

Based on the error analysis, the authors proposed a new kind of high accuracy boundary element method (BEM) (HABEM), and for the large-scale problems, the fast algorithm, such as…

Abstract

Purpose

Based on the error analysis, the authors proposed a new kind of high accuracy boundary element method (BEM) (HABEM), and for the large-scale problems, the fast algorithm, such as adaptive cross approximation (ACA) with generalized minimal residual (GMRES) is introduced to develop the high performance BEM (HPBEM). It is found that for slender beams, the stress analysis using iterative solver GMRES will difficult to converge. For the analysis of slender beams and thin structures, to enhance the efficiency of GMRES solver becomes a key problem in the development of the HPBEM. The purpose of this paper is study on the preconditioning method to solve this convergence problem, and it is started from the 2D BE analysis of slender beams.

Design/methodology/approach

The conventional sparse approximate inverse (SAI) based on adjacent nodes is modified to that based on adjacent nodes along the boundary line. In addition, the authors proposed a dual node variable merging (DNVM) preprocessing for slender thin-plate beams. As benchmark problems, the pure bending of thin-plate beam and the local stress analysis (LSA) of real thin-plate cantilever beam are applied to verify the effect of these two preconditioning method.

Findings

For the LSA of real thin-plate cantilever beams, as GMRES (m) without preconditioning applied, it is difficult to converge provided the length to height ratio greater than 50. Even with the preconditioner SAI or DNVM, it is also difficult to obtain the converged results. For the slender real beams, the iteration of GMRES (m) with SAI or DNVM stopped at wrong deformation state, and the computation failed. By changing zero initial solution to the analytical displacement solution of conventional beam theory, GMRES (m) with SAI or DNVM will not be stopped at wrong deformation state, but the stress error is still difficult to converge. However, by GMRES (m) combined with both SAI and DNVM preconditioning, the computation efficiency enhanced significantly.

Originality/value

This paper presents two preconditioners: DNVM and a modified SAI based on adjacent nodes along the boundary line of slender thin-plate beam. In the LSA, by using GMRES (m) combined with both DNVM and SAI, the computation efficiency enhanced significantly. It provides a reference for the further development of the 3D HPBEM in the LSA of real beam, plate and shell structures.

Details

Engineering Computations, vol. 36 no. 8
Type: Research Article
ISSN: 0264-4401

Keywords

Article
Publication date: 29 April 2014

Guoyun Zhou, Chia-Yun Chen, Liyi Li, Zhihua Tao, Wei He and C.P. Wong

Nickel phosphorus (Ni−P) thin-films have been electrolessly deposited in an acid-plating bath with the addition of manganese sulfate monohydrate (MSM) to achieve higher resistance…

Abstract

Purpose

Nickel phosphorus (Ni−P) thin-films have been electrolessly deposited in an acid-plating bath with the addition of manganese sulfate monohydrate (MSM) to achieve higher resistance for the application of embedded resistor with value beyond 10 KΩ. As this material is being used for fabricating embedded resistors under the addition of MSM, its resistance properties including effects of MSM concentration and plating time on resistances, temperature coefficient of resistance (TCR), and resistance tolerance of embedded resistor were investigated. The paper aims to discuss these issues.

Design/methodology/approach

The structure of fabricated Ni−P film was detected by means of scanning electron microscopy (SEM) and transmission electron microscopy (TEM). The properties of substrate, including the surface morphologies, glass transition process and boundary of copper pad and substrate surface, were performed by SEM, dynamic mechanical analysis and optical microscope, respectively. The resistance tolerances of embedded resistors were elaborated from the cases of Ni−P thin-film resistance tolerance and the size effects of resistors, respectively.

Findings

The fabricated film was found to be constructed with numerous Ni−P amorphous nanoparticles, which was believed to be the reason of increasing thin-film resistance. The Ni−P thin-films presented over one magnitude order of resistance increasing in the case of MSM concentration varied from 0 to 40 g/L. For the case of TCRs, Ni−P thin-films deposited with 20 g/L MSM exhibited low TCRs of within ±100 ppm/°C Before TR at temperature elevating from 40 to 160°C, indicating that this Ni−P thin-film belongs to the constant TCR materials according to the military standard. For the tolerance of embedded resistor, the tolerance contributed by Ni−P thin-film was obtained to be 9.8 percent, whereas the geometry tolerances were in the range of 0-20 percent according to the geometries of embedded resistor.

Originality/value

For Ni−P thin-film without MSM, its low resistance with around 100 ohm/sq. limit the values of resistor few KΩ and restricted its widespread application of embedded resistor with higher resistance beyond 10 KΩ. The authors introduced MnSO4 in Ni−P electroless plating process to improve the low resistance of Ni−P thin-film. The resistance was increased over one order of magnitude after added with 40 g/L MnSO4. Due to the specific structure, as this material is being used for fabricating embedded resistors, the electrical properties and its application properties to verify its appliance in embedded resistor were systematically investigated by means of SEM, TEM, XRD characterizations, TCRs, resistance tolerance analysis, respectively.

Article
Publication date: 1 December 2002

Virgiliu Fireteanu, Bernard Paya, Jacques Nuns and Tiberiu Tudorache

This paper analyses the conditions for which the results of eddy currents computation in thin regions modelled by surface regions are concordant with those obtained using volume…

Abstract

This paper analyses the conditions for which the results of eddy currents computation in thin regions modelled by surface regions are concordant with those obtained using volume finite elements. The concepts of geometrically thin or thick region, electromagnetically thin or thick region, 2D or 3D problem, transverse or longitudinal flux problem are used to characterise the limits of the surface model. The computation of eddy currents in sheets heated in transverse flux inductors and of the eddy current losses in metallic casing of an induction furnace highlights the surface finite element applicability.

Details

COMPEL - The international journal for computation and mathematics in electrical and electronic engineering, vol. 21 no. 4
Type: Research Article
ISSN: 0332-1649

Keywords

Article
Publication date: 1 February 2000

Richard Friedrich

This bibliography contains references to papers, conference proceedings, theses and books dealing with finite strip, finite prism and finite layer analysis of structures…

1193

Abstract

This bibliography contains references to papers, conference proceedings, theses and books dealing with finite strip, finite prism and finite layer analysis of structures, materially and/or geometrically linear or non‐linear.

Details

Engineering Computations, vol. 17 no. 1
Type: Research Article
ISSN: 0264-4401

Keywords

Article
Publication date: 20 December 2017

Haidong Yu, Chunzhang Zhao, Bin Zheng and Hao Wang

Thin-walled structures inevitably always have manufacturing deviations, which affects the assembly quality of mechanical products. The assembly quality directly determines the…

Abstract

Purpose

Thin-walled structures inevitably always have manufacturing deviations, which affects the assembly quality of mechanical products. The assembly quality directly determines the performances, reliability and service life of the products. To achieve the automatic assembly of large-scale thin-walled structures, the sizing force of the structures with deviations should be calculated, and its assembling ability should be studied before assembly process. The purpose of this study is to establish a precise model to describe the deviations of structures and to study the variation propagation during assembly process.

Design/methodology/approach

Curved thin-walled structures are modeled by using the shell element via the absolute nodal coordinate formulation. Two typical deviation modes of the structure are defined. The generalized elastic force of shell elements with anisotropic materials is deduced based on a continuum mechanics approach to account for the geometric non-linearity. The quasi-static method is introduced to describe the assembly process. The effects of the deviation forms, geometrical parameters of the thin-walled structures and material properties on assembly quality are investigated numerically.

Findings

The geometric non-linearity of structure and anisotropy of materials strongly affect the variation propagation and the assembly quality. The transformation and accumulation effects of the deviations are apparent in the multiple assembly process. The constraints on the structures during assembly can reduce assembly deviation.

Originality/value

The plate element via the absolute nodal coordinate formulation is first introduced to the variation propagation analysis. Two typical shape deviation modes are defined. The elastic force of structures with anisotropic materials is deduced. The variation propagation during the assembly of structures with various geometrical and material parameters is investigated.

Article
Publication date: 2 January 2009

Uroš Bohinc, Adnan Ibrahimbegovic and Boštjan Brank

The purpose of this paper is to address error‐controlled adaptive finite element (FE) method for thin and thick plates. A procedure is presented for determining the most suitable…

Abstract

Purpose

The purpose of this paper is to address error‐controlled adaptive finite element (FE) method for thin and thick plates. A procedure is presented for determining the most suitable plate model (among available hierarchical plate models) for each particular FE of the selected mesh, that is provided as the final output of the mesh adaptivity procedure.

Design/methodology/approach

The model adaptivity procedure can be seen as an appropriate extension to model adaptivity for linear elastic plates of so‐called equilibrated boundary traction approach error estimates, previously proposed for 2D/3D linear elasticity. Model error indicator is based on a posteriori element‐wise computation of improved (continuous) equilibrated boundary stress resultants, and on a set of hierarchical plate models. The paper illustrates the details of proposed model adaptivity procedure for choosing between two most frequently used plate models: the one of Kirchhoff and the other of Reissner‐Mindlin. The implementation details are provided for a particular case of the discrete Kirchhoff quadrilateral four‐node plate FE and the corresponding Reissner‐Mindlin quadrilateral with the same number of nodes. The key feature for those elements that they both provide the same quality of the discretization space (and thus the same discretization error) is the one which justifies uncoupling of the proposed model adaptivity from the mesh adaptivity.

Findings

Several numerical examples are presented in order to illustrate a very satisfying performance of the proposed methodology in guiding the final choice of the optimal model and mesh in analysis of complex plate structures.

Originality/value

The paper confirms that one can make an automatic selection of the most appropriate plate model for thin and thick plates on the basis of proposed model adaptivity procedure.

Details

Engineering Computations, vol. 26 no. 1/2
Type: Research Article
ISSN: 0264-4401

Keywords

Article
Publication date: 21 September 2023

Sifeddine Abderrahmani

Among different types of engineering structures, plates play a significant role. Their analysis necessitates numerical modeling with finite elements, such as triangular…

Abstract

Purpose

Among different types of engineering structures, plates play a significant role. Their analysis necessitates numerical modeling with finite elements, such as triangular, quadrangular or sector plate elements, owing to the intricate geometrical shapes and applied loads. The scope of this study is the development of a new rectangular finite element for thin plate bending based on the strain approach using Airy's function. It is called a rectangular plate finite element using Airy function (RPFEUAF) and has four nodes. Each node had three degrees of freedom: one transverse displacement (w) and two normal rotations (x, y).

Design/methodology/approach

Equilibrium conditions are used to generate the interpolation functions for the fields of strain, displacements and stresses. The evolution of the Airy function solutions yielded the selection of these polynomial bi-harmonic functions. The variational principle and the analytical integration approach are used to evaluate the basic stiffness matrix.

Findings

The numerical findings for thin plates quickly approach the Kirchhoff solution. The results obtained are compared to the analytical solution based on Kirchhoff theory.

Originality/value

The efficiency of the strain based approach using Airy's function is confirmed, and the robustness of the presented element RPFEUAF is demonstrated. Because of this, the current element is more reliable, better suited for computations and especially intriguing for modeling this kind of structure.

Details

International Journal of Structural Integrity, vol. 14 no. 6
Type: Research Article
ISSN: 1757-9864

Keywords

Article
Publication date: 12 July 2023

Xin Su, Eburilitu Bai and Guojun Hai

A unified framework for solving the bending, buckling and vibration problems of rectangular thin plates (RTPs) with four free edges (FFFF), including isotropic RTPs, orthotropic…

Abstract

Purpose

A unified framework for solving the bending, buckling and vibration problems of rectangular thin plates (RTPs) with four free edges (FFFF), including isotropic RTPs, orthotropic rectangular thin plates (ORTPs) and nano-rectangular plates, is established by using the symplectic superposition method (SSM).

Design/methodology/approach

The original fourth-order partial differential equation is first rewritten into Hamiltonian system. The class of boundary value problems of the original equation is decomposed into three subproblems, and each subproblem is given the corresponding symplectic eigenvalues and symplectic eigenvectors by using the separation variable method in Hamiltonian system. The symplectic orthogonality and completeness of symplectic eigen-vectors are proved. Then, the symplectic eigenvector expansion method is applied to solve the each subproblem. Then, the symplectic superposition solution of the boundary value problem of the original fourth-order partial differential equation is given through superposing analytical solutions of three foundation plates.

Findings

The bending, vibration and buckling problems of the rectangular nano-plate/isotropic rectangular thin plate/orthotropic rectangular thin plate with FFFF can be solved by the unified symplectic superposition solution respectively.

Originality/value

The symplectic superposition solution obtained is a reference solution to verify the feasibility of other methods. At the same time, it can be used for parameter analysis to deeply understand the mechanical behavior of related RTPs. The advantages of this method are as follows: (1) It provides a systematic framework for solving the boundary value problem of a class of fourth-order partial differential equations. It is expected to solve more complicated boundary value problems of partial differential equations. (2) SSM uses series expansion of symplectic eigenvectors to accurately describe the solution. Moreover, symplectic eigenvectors are orthogonal and directly reflect the orthogonal relationship of vibration modes. (3) The SSM can be carried to bending, buckling and free vibration problems of the same plate with other boundary conditions.

Details

Engineering Computations, vol. 40 no. 6
Type: Research Article
ISSN: 0264-4401

Keywords

Article
Publication date: 23 March 2012

Sandeep Singh, Kamlesh Kulkarni, Ramesh Pandey and Harpreet Singh

The purpose of this paper is to present elastic buckling behaviour of simply supported and clamped thin rectangular isotropic plates having central circular cutouts subjected to…

Abstract

Purpose

The purpose of this paper is to present elastic buckling behaviour of simply supported and clamped thin rectangular isotropic plates having central circular cutouts subjected to uniaxial partial edge compression. Analysis is carried out for four different kinds of partial edge compression and it is extended to study the effect of aspect ratio of plate on buckling load.

Design/methodology/approach

A finite element method technique is used in the current work to solve the buckling problem of plate using eight node quadrilateral element and plate kinematics based on first order shear deformation theory. Results obtained from finite element analysis are first validated for isotropic square plates, without cutouts, subjected to uniaxial partial edge compression with some earlier published literature.

Findings

From the current work it is concluded that the buckling strength of square plates is highly influenced by partial edge compression, as compared to plate subjected to uniform edge compression; but with increase in aspect ratio, influence of partial edge compression on plate buckling load decreases.

Originality/value

This paper usefully shows how partial edge compression of plates affects the buckling strength of plate having circular cutouts. Generally, simply supported plates subjected uniaxial partial edge compression of Type I and Type III are found to be stronger than plates subjected to partial edge compression Type II and Type IV, respectively.

Details

Journal of Engineering, Design and Technology, vol. 10 no. 1
Type: Research Article
ISSN: 1726-0531

Keywords

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