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Article
Publication date: 6 August 2020

Niu-Jing Ma, Li-Xiong Gu, Long Piao and Xing-Zhi Zhang

Stiffened plates have been widely used in civil, marine, aerospace engineering. As a kind of thin-walled structure operating in complex environment, stiffened plates

Abstract

Purpose

Stiffened plates have been widely used in civil, marine, aerospace engineering. As a kind of thin-walled structure operating in complex environment, stiffened plates mostly undergo a variety of dynamic loads, which may sometimes result in large-amplitude vibration. Additionally, initial stresses and geometric imperfections are widespread in this type of structure. Furthermore, it is universally known that initial stresses and geometric imperfections may affect mechanical behavior of structures severely, particularly in dynamic analysis. Thus, the purpose of this paper is to study the stress variation rule of a stiffened plate during large-amplitude vibration considering initial stresses and geometric imperfections.

Design/methodology/approach

The initial stresses are represented in the form of initial bending moments applying to the stiffened plate, while the initial geometric imperfections are considered by means of trigonometric series, and they are assumed existing in the plate along the z-direction exclusively. Then, the dynamic equilibrium equations of the stiffened plate are established using Lagrange’s equation as well as aforementioned conditions. The nonlinear differential equations of motion are simplified as a two-degree-of-freedom system by considering 1:2 and 1:3 internal resonances, respectively, and the multiscale method is applied to solve the equations.

Findings

The influence of initial stresses on the plate, stresses during internal resonance is remarkable, while that is moderate for initial geometric imperfections. (Upon considering the existence of initial stresses or geometric imperfections, the stresses of motivated modes are less than the primary mode for both and internal resonances). The influence of bidirectional initial stresses on the plate’s stresses during internal resonance is more remarkable than that of unidirectional initial stresses. The coupled vibration in 1%3A2 internal resonance is fiercer than that in internal resonance.

Originality/value

Stiffened plates are widely used in engineering structures. However, as a type of thin-walled structure, stiffened plates vibrate with large amplitude in most cases owning to their complicated operation circumstance. In addition, stiffened plates usually contain initial stresses and geometric imperfections, which may result in the variation of their mechanical behavior, especially dynamical behavior. Based on the above consideration, this paper studies the nonlinear dynamical behavior of stiffened plates with initial stresses and geometrical imperfections under different internal resonances, which is the originality of this work. Furthermore, the research findings can provide references for engineering design and application.

Details

Engineering Computations, vol. 38 no. 2
Type: Research Article
ISSN: 0264-4401

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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…

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

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Article
Publication date: 1 May 2000

Jaroslav Mackerle

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

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.

Details

Engineering Computations, vol. 17 no. 3
Type: Research Article
ISSN: 0264-4401

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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…

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

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Article
Publication date: 1 May 1995

L. Jiang and M.W. Chernuka

A stiffened shell element is presented for geometricallynon‐linear analysis of eccentrically stiffened shell structures.Modelling with this element is more accurate than…

Abstract

A stiffened shell element is presented for geometrically non‐linear analysis of eccentrically stiffened shell structures. Modelling with this element is more accurate than with the traditional equivalent orthotropic plate element or with lumping stiffeners. In addition, mesh generation is easier than with the conventional finite element approach where the shell and beam elements are combined explicitly to represent stiffened structures. In the present non‐linear finite element procedure, the tangent stiffness matrix is derived using the updated Lagrangian formulation and the element strains, stresses, and internal force vectors are updated employing a corotational approach. The non‐vectorial characteristic of large rotations is taken into account. This stiffened shell element formulation is ideally suited for implementation into existing linear finite element programs and its accuracy and effectiveness have been demonstrated in several numerical examples.

Details

Engineering Computations, vol. 12 no. 5
Type: Research Article
ISSN: 0264-4401

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Article
Publication date: 1 August 2002

Jaroslav Mackerle

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…

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.

Details

Engineering Computations, vol. 19 no. 5
Type: Research Article
ISSN: 0264-4401

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Article
Publication date: 21 March 2008

Namita Nanda and J.N. Bandyopadhyay

To investigate the large amplitude free flexural vibration of doubly curved shallow shells in the presence of cutouts.

Abstract

Purpose

To investigate the large amplitude free flexural vibration of doubly curved shallow shells in the presence of cutouts.

Design/methodology/approach

Finite element model using an eight‐noded C0 continuity, isoparametric quadrilateral element is employed. Nonlinear strains of von Karman type are incorporated into the first‐order shear deformation theory.

Findings

Cylindrical shell shows mostly hard spring behavior whereas spherical shell shows both hard spring and soft spring behavior with the increase of amplitude ratios for different cutout sizes, radii of curvature and thickness parameters. At a particular value of the amplitude ratio, the frequency ratio of shells is governed by the interactive effects of stiffness and mass.

Practical implications

Aircraft, spacecraft and many other structures where shell panels are used, undergo large amplitude nonlinear vibrations.

Originality/value

The paper will assist researchers of vibration behavior of elastic systems.

Details

Aircraft Engineering and Aerospace Technology, vol. 80 no. 2
Type: Research Article
ISSN: 0002-2667

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Article
Publication date: 4 July 2016

Nasrin Jafari and Mojtaba Azhari

The purpose of this paper is to present a simple HP-cloud method as an accurate meshless method for the geometrically nonlinear analysis of thick orthotropic plates of…

Abstract

Purpose

The purpose of this paper is to present a simple HP-cloud method as an accurate meshless method for the geometrically nonlinear analysis of thick orthotropic plates of general shape. This method is used to investigate the effects of thickness, geometry of various shapes, boundary conditions and material properties on the large deformation analysis of Mindlin plates.

Design/methodology/approach

Nonlinear analysis of plates based on Mindlin theory is presented. The equations are derived by the Von-Karman assumption and total Lagrangian formulations. Newton-Raphson method is applied to achieve linear equations from nonlinear equations. Simple HP-cloud method is used for the construction of the shape functions based on Kronecker-δ properties, so the essential boundary conditions can be enforced directly. Shepard function is utilized for a partition of unity and complete polynomial is used as an enrichment function.

Findings

The suitability and efficiency of the simple HP-cloud method for the geometrically nonlinear analysis of thin and moderately thick plates is studied for the first time. Large displacement analysis of various shapes of plates, rectangular, skew, trapezoidal, circular, hexagonal and triangular with different boundary conditions subjected to distributed loading are considered.

Originality/value

This paper shows that the simple HP-cloud method is well suited for the large deformation analysis of Mindlin plates with various geometries, because it uses a set of a few arbitrary nodes placed in a plate of general shape. Moreover the convergence rate of the proposed method is high and the cost of solving equations is low.

Details

Engineering Computations, vol. 33 no. 5
Type: Research Article
ISSN: 0264-4401

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Article
Publication date: 1 March 2002

Jaroslav Mackerle

Gives a bibliographical review of the finite element analyses of sandwich structures from the theoretical as well as practical points of view. Both isotropic and composite…

Abstract

Gives a bibliographical review of the finite element analyses of sandwich structures from the theoretical as well as practical points of view. Both isotropic and composite materials are considered. Topics include: material and mechanical properties of sandwich structures; vibration, dynamic response and impact problems; heat transfer and thermomechanical responses; contact problems; fracture mechanics, fatigue and damage; stability problems; special finite elements developed for the analysis of sandwich structures; analysis of sandwich beams, plates, panels and shells; specific applications in various fields of engineering; other topics. The analysis of cellular solids is also included. The bibliography at the end of this paper contains 655 references to papers, conference proceedings and theses/dissertations dealing with presented subjects that were published between 1980 and 2001.

Details

Engineering Computations, vol. 19 no. 2
Type: Research Article
ISSN: 0264-4401

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Article
Publication date: 1 January 1979

DAVID I.G. JONES

The aim of this paper is to review, briefly and selectively, some highlights of the progress made in the development of damping materials technology for vibration control…

Abstract

The aim of this paper is to review, briefly and selectively, some highlights of the progress made in the development of damping materials technology for vibration control, in the past two decades, with particular emphasis on the developments sponsored by the US Air Force Materials Laboratory at Wright‐Patterson Air Force Base.

Details

Aircraft Engineering and Aerospace Technology, vol. 51 no. 1
Type: Research Article
ISSN: 0002-2667

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