Dynamic and Stress Analyisis of Spatial Flexible Mechanical Systems

1992 ◽  
Author(s):  
J. M. Kremer ◽  
A. A. Shabana ◽  
G. E. O. Widera
Keyword(s):  
Rigid Body ◽  
Arbitrary Number ◽  
Mass Matrix ◽  
Laminated Composite ◽  
Composite Plates ◽  
The Body ◽  
Element Formulation ◽  
Stiffness Matrices ◽  
Rigid Body Modes ◽  
Orthotropic Material Property

Abstract This investigation concerns itself with the dynamic and stress analysis of thin, laminated composite plates consisting of layers of orthotropic laminae. It is assumed that the bonds between the laminae are infinitesimally thin and shear nondeformable. The finite element formulation presented is sufficiently general to accept an arbitrary number of layers and an arbitrary number of orthotropic material property sets. In the dynamic formulation presented, the laminae is assumed to undergo large arbitrary rigid body displacements and small elastic deformations. The nodal shape functions of the laminae are assumed to have rigid body modes that need to describe only large rigid body translations. Using the expressions for the kinetic and strain energies, the lamina mass and stiffness matrices are identified. The nonlinear mass matrix of the lamina is expressed in terms of a set of invariants that depend on the assumed displacement field. By summing the laminae kinetic and strain energies, the body mass and stiffness matrices are identified. It is shown that the body invariants can be expressed explicitly in terms of the invariants of its laminae. Numerical examples of a spatial RSSR mechanism demonstrate the use of the present formulation.

Application of Composite Plate Theory and the Finite Element Method to the Dynamics and Stress Analysis of Spatial Flexible Mechanical Systems

1994 ◽  
Vol 116 (3) ◽  
pp. 952-960 ◽  
Author(s):  
J. M. Kremer ◽  
A. A. Shabana ◽  
G. E. O. Widera
Keyword(s):  
Finite Element ◽  
Rigid Body ◽  
Stress Analysis ◽  
Arbitrary Number ◽  
Plate Theory ◽  
Mass Matrix ◽  
Composite Plates ◽  
The Body ◽  
Element Formulation ◽  
Stiffness Matrices

This investigation concerns itself with the dynamic and stress analysis of thin, laminated composite plates consisting of layers of orthotropic laminae. It is assumed that the bonds between the laminae are infinitesimally thin and shear nondeformable. The finite element formulation presented is sufficiently general to accept an arbitrary number of layers and an arbitrary number of orthotropic material property sets. In the dynamic formulation presented, the laminae is assumed to undergo large arbitrary rigid body displacements and small elastic deformations. The nodal shape functions of the laminae are assumed to have rigid body modes that need to describe only large rigid body translations. Using the expressions for the kinetic and strain energies, the lamina mass and stiffness matrices are identified. The nonlinear mass matrix of the lamina is expressed in terms of a set of invariants that depend on the assumed displacement field. By summing the laminae kinetic and strain energies, the body mass and stiffness matrices are identified. It is shown that the body invariants can be expressed explicitly in terms of the invariants of its laminae. Numerical examples of a spatial RSSR mechanism are presented in order to demonstrate the use of the present formulation.

Vibration Behavior of Thick Composite Laminated Plates Subject to In-Plane Pre-Stress Loading

2007 ◽  
Author(s):  
Lars Fiedler ◽  
Walter Lacarbonara ◽  
Fabrizio Vestroni
Keyword(s):  
Mass Matrix ◽  
Laminated Composite ◽  
Composite Plates ◽  
Order Theory ◽  
Laminated Plates ◽  
Energy Functionals ◽  
Vibration Behavior ◽  
Stiffness Matrices ◽  
Polynomial Series ◽  
Higher Order Theory

The vibration behavior of rectangular laminated composite plates subject to in-plane loading is investigated employing a global higher-order theory. The displacement field is expanded in the thickness direction in a complete polynomial series with arbitrary degree whereas the series coefficients, function of the in-plane coordinates, are expressed, according to Ritz’s method, as a superposition of admissible functions. The elastic and geometric stiffness matrices as well as the mass matrix are obtained from the energy functionals in terms of the generalized coordinates. The problem is suitably nondimensionalized so as to single out the independent parameters. Variations of the lowest frequencies with the width-to-thickness ratio and with the ratio between the in-plane elastic moduli are investigated to ascertain the sensitivity of the vibration behavior with respect to these parameters. Effects of the lamination scheme on the vibration properties are assessed.

A cell-based smoothed finite element formulation for viscoelastic laminated composite plates considering hygrothermal effects

2020 ◽  
pp. 002199832098005
Author(s):  
Sy-Ngoc Nguyen ◽  
Tam T Truong ◽  
Maenghyo Cho ◽  
Nguyen-Thoi Trung
Keyword(s):  
Finite Element ◽  
Shear Deformation Theory ◽  
Laminated Composite ◽  
Composite Plates ◽  
Integral Form ◽  
Complex Stress ◽  
Laminated Plates ◽  
Element Formulation ◽  
Composite Laminated Plates ◽  
Smoothed Finite Element Method

In the present study, the viscoelastic analysis is investigated for composite laminated plates using a smoothed finite element method called cell/element based smoothed discrete shear gap method. Moreover, the hygrothermal effects is considered on the viscoelastic responses of composite laminated plates. The first-order shear deformation theory is employed due to its simplicity and accuracy. With the help of the convolution theorem in Laplace transformation, the complex stress-strain relationship in integral form is simplified to linear in transformed domain. Therefore, all computing procedures are performed in the transformed domain and then, using inverse techniques (Fast Fourier Transform) to converted back to the real-time domain. The study provides an effective computational tool to analyze the viscoelastic response of laminated composite taking into account the influence of the time and hygrothermal effects.

scholarly journals An Efficient Modelling of Flexible Airships

2006 ◽  
Author(s):  
Selima Bennaceur ◽  
Naoufel Azouz ◽  
Djaber Boukraa
Keyword(s):  
Rigid Body ◽  
Equations Of Motion ◽  
General System ◽  
Rigid Body Motion ◽  
The Body ◽  
Body Motion ◽  
Modal Synthesis ◽  
Stiffness Matrices ◽  
Updated Lagrangian ◽  
Convenient Technique

This paper presents an efficient modelling of airships with small deformations moving in an ideal fluid. The formalism is based on the Updated Lagrangian Method (U.L.M.). This formalism proposes to take into account the coupling between the rigid body motion and the deformation as well as the interaction with the surrounding fluid. The resolution of the equations of motion is incremental. The behaviour of the airship is defined relatively to a virtual non-deformed reference configuration moving with the body. The flexibility is represented by a deformation modes issued from a Finite Elements Method analysis. The increment of rigid body motion is represented similarly by rigid modes. A modal synthesis is used to solve the general system equations of motion. Time constant matrices appears (i.e. mass and structural stiffness matrices), and we show a convenient technique to actualise the time dependant matrices.

scholarly journals Thermal Post-Buckling Improvements of Laminated Composite Plates Using the Active Strain Energy Tuning Approach

2011 ◽  
Vol 311-313 ◽  
pp. 2235-2238
Author(s):  
Zainudin A Rasid ◽  
Rizal Zahari ◽  
Ayob Amran ◽  
Dayang Laila Majid ◽  
Ahmad Shakrine M. Rafie
Keyword(s):  
Finite Element ◽  
Shape Memory Alloy ◽  
Shape Memory Alloys ◽  
Shape Memory ◽  
Strain Energy ◽  
Laminated Composite ◽  
Composite Plates ◽  
Element Formulation ◽  
Laminated Composite Plates ◽  
Post Buckling

Shape memory alloy was firstly used commercially as a hydraulic coupling in the Grumman F14A in 1971. It is today used among others to improve structural behaviours such as buckling of composite plates in the aerospace vehicles. In this paper, finite element model and its source code for thermal post-buckling of shape memory alloy laminated composite plates is presented. The shape memory alloy wires induced stress that improved the strain energy, stiffness and thus the buckling behaviour of the composite plates. The finite element formulation catered the combined properties of the composite and shape memory alloys, the addition of the recovery stress and the temperature dependent properties of the shape memory alloys and the composite matrix. This study showed that by embedding shape memory alloy within layers of composite plates, post-buckling behaviours of composite plates can be improved substantially.

scholarly journals Thermal Buckling and Post-Buckling Improvements of Laminated Composite Plates Using Finite Element Method

2011 ◽  
Vol 471-472 ◽  
pp. 536-541 ◽  
Author(s):  
Zainudin A. Rasid ◽  
Ayob Amran ◽  
Rizal Zahari ◽  
Faizal Mustapha ◽  
D.L. Majid ◽  
...  
Keyword(s):  
Finite Element ◽  
Shape Memory Alloy ◽  
Shape Memory ◽  
Laminated Composite ◽  
Composite Plates ◽  
Thermal Buckling ◽  
Element Formulation ◽  
Laminated Composite Plates ◽  
Aerospace Applications ◽  
Post Buckling

Thermal buckling and thermal post-buckling behaviours of laminated composite plates are improved by embedding shape memory alloy wires within laminates of composite plates. The procedure is to use the recovery stress that is induced when the reverse transformation of the shape memory alloy from martensite to austenite phases is constrained. For aerospace applications where the source of the shape memory alloy heating is the high temperature environment itself, a study is conducted to see the effect of shape memory alloy in improving the thermal buckling and post-buckling of composite plates. Due to the temperature dependent nature of the composite matrix and the shape memory alloy, the finite element formulation developed here is in the incremental form. Solving this non-linear model using the developed in-house source code, critical loads are determined and the post-buckling paths of the shape memory alloy composite plates are traced. This study shows that by embedding the shape memory alloy within composite plates, the thermal buckling and post-buckling behaviours of composite plates can be improved substantially.

Modelling lateral manoeuvres in fish

2012 ◽  
Vol 697 ◽  
pp. 1-34 ◽  
Author(s):  
K. Singh ◽  
T. J. Pedley
Keyword(s):  
Rigid Body ◽  
Equations Of Motion ◽  
Rigid Body Dynamics ◽  
The Body ◽  
Body Motion ◽  
Dynamic State ◽  
Parameter Study ◽  
Element Formulation ◽  
Turn Angle ◽  
Impulsive Input

AbstractWe propose a method to model manoeuvres in self-propelled flexible-bodied fish by modelling the hydrodynamics coupled to the body inertia. Flexible body motion is prescribed and the equations of motion are solved for the position of the centre of mass and rotation of the body. The governing equations are formulated by applying the conservation of linear and angular momentum. Two independent methods to model the fluid dynamics are pursued: Model 1 is an extension of elongated-body theory, modified for self-propulsion and flexible motion. Model 2 applies a numerical boundary-element formulation with the fish modelled as an infinitely thin rectangular body. The manoeuvring response to an impulsive input is first examined to understand the rigid-body characteristics of the fish. A flexible bend action is included to model C-bends of the type observed during escapes in fish. Models 1 and 2 are used to cross-verify the respective implementations as well as to develop physical insights into manoeuvring. A parameter study shows that fish of intermediate body depths are best adapted to rapid turns whereas the initial dynamic state of the fish is instrumental in affecting the sign as well as the magnitude of the turn angle, for a prescribed bend deflection. Computations for combined swimming and turning show that the initial rigid-body dynamics of the fish is much more effective than the induced effect of the prior shed wake in enhancing the turning response.

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