A Finite Element Formulation for the Dynamic Analysis of Machine Components Fabricated From Composite Materials

1992 ◽  
Author(s):  
A. Semos ◽  
C. Chassapis
Keyword(s):  
Finite Element ◽  
Composite Materials ◽  
Dimensional Space ◽  
Equations Of Motion ◽  
Three Dimensional ◽  
Laminated Composite ◽  
Element Formulation ◽  
Reinforced Composite ◽  
External Forces ◽  
Three Dimensional Space

Abstract In this paper finite element procedures are presented for analyzing the elastic-dynamic behavior of mechanical components fabricated from fiber-reinforced composite materials. An arbitrarily laminated composite plate element is created which allows the analysis of components that are moving in three dimensional space. The five D.O.F. per node static model of S. C. Panda and R. Natarajan is used as a basis for the derivation of the dynamic model. The elemental equations of motion are derived from Hamilton’s Principle. The formulation considers the total kinetic and strain energies of the moving element, together with the work due to bending, caused by the transversely acting external forces, as well as that due to the foreshortening of the element, caused by axially applied loads.

scholarly journals A Finite Element Formulation for Fluid-Structure Interaction in Three-Dimensional Space

1981 ◽  
Vol 103 (2) ◽  
pp. 183-190 ◽  
Author(s):  
R. F. Kulak
Keyword(s):  
Finite Element ◽  
Dimensional Space ◽  
Equations Of Motion ◽  
Fluid Structure Interaction ◽  
Three Dimensional ◽  
Element Formulation ◽  
Fluid Structure ◽  
Structure Interaction ◽  
Discrete Equations ◽  
Numerical Predictions

In this paper a development is presented for a three-dimensional hexahedral hydrodynamic finite-element. Using trilinear shape functions and assuming a constant pressure field in each element, simple relations were obtained for internal nodal forces. Because the formulation was based upon a rate approach it was applicable to problems involving large displacements. This element was incorporated into an existing plate-shell finite element code. Diagonal mass matrices were used and the resulting discrete equations of motion were solved using an explicit temporal integrator. Results for several problems were presented which compare numerical predictions to closed form analytical solutions. In addition, the fluid-structure interaction problem of a fluid-filled, cylindrical vessel containing internal cylinders was studied. The internal cylinders were cantilever supported from the top cover of the vessel and were periodically located circumferentially at a fixed radius. A pressurized cylindrical cavity located at the bottom of the vessel at its centerline provided the loading.

Energy Harvesting Aspects of Irregular Vibrating Forces Acting on Piezoelectric Devices

2015 ◽  
pp. 143-158
Author(s):  
Alessandro Massaro
Keyword(s):  
Energy Harvesting ◽  
Piezoelectric Materials ◽  
Dimensional Space ◽  
Three Dimensional ◽  
Output Current ◽  
Vibrating System ◽  
External Forces ◽  
Piezoelectric Devices ◽  
Three Dimensional Space

After a brief introduction of piezoelectric materials, this chapter focuses on the characterization of vibrating freestanding piezoelectric AlN devices forced by different external forces acting simultaneously. The analyzed vibrating forces are applied mainly to piezoelectric freestanding structures stimulated by irregular vibration phenomena. Particular kinds of theoretical noise signals are commented. The goal of the chapter is to analyze the effect of the noise in order to model the chaotic vibrating system and to predict the output current signals. Moreover, the author also shows a possible alternative way to detect different vibrating force directions in the three dimensional space by means of curved piezoelectric layouts.

Mechanical Behavior of Laminated Composites with Circular Holes

2013 ◽  
Vol 550 ◽  
pp. 1-8 ◽  
Author(s):  
Habib Achache ◽  
Benali Boutabout ◽  
Djamel Ouinas
Keyword(s):  
Finite Element ◽  
Stress Concentration ◽  
Composite Structures ◽  
Laminated Composites ◽  
Three Dimensional ◽  
Laminated Composite ◽  
Element Formulation ◽  
Composites Materials ◽  
Circular Holes ◽  
Fibers Orientation

This paper presents a numerical method for the evaluation of the stress concentration factor (SCF) in three dimensional laminated composites under mechanical loads. The proposed method uses the finite element formulation. The composites materials based on the epoxy matrix and reinforcing fibers are extensively used in aircraft structures due to their high specific characteristics. However, the withstanding of composite structures can be significantly reduced by the addition of geometric singularities, such as perforations or notches. To Analyses the stress concentration around geometrical notches, several studies as analytical, numerical and experimental techniques are available. The stress distribution in a laminated composite plate with the presence of a circular hole was investigated using the finite element method. In order, the results obtained by this study are compared with those reported in literature. The aim of this analysis is to evaluate numerically the factor of stress concentration under the influence of several parameters such as fibers orientation, the mechanical characteristics of composites and the distance between notches of cross-laminated.

Closed-Form Primitives for Generating Volume Preserving Deformations

1993 ◽  
Author(s):  
Gregory S. Chirikjian
Keyword(s):  
Closed Form ◽  
Dimensional Space ◽  
Equations Of Motion ◽  
Three Dimensional ◽  
Physical Systems ◽  
Mechanics Of Materials ◽  
Time Simulation ◽  
Infinite Variety ◽  
Volume Preserving ◽  
Three Dimensional Space

Abstract In this paper, methods for generating closed-form expressions for locally volume preserving deformations of general volumes in three dimensional space are introduced. These methods potentially have applications to computer aided geometric design, the mechanics of materials, and realistic real-time simulation and animation of physical processes. In mechanics, volume preserving deformations are intimately related to the conservation of mass. The importance of this fact manifests itself in design, and in the realistic simulation of many physical systems. Whereas volume preservation is generally written as a constraint on equations of motion in continuum mechanics, this paper develops a set of physically meaningful basic deformations which are intrinsically volume preserving. By repeated application of these primitives, an infinite variety of deformations can be written in closed form.

Nonlinear Finite-Element Method for Plates and Its Application to Dynamic Response of Reactor Fuel Subassemblies

1974 ◽  
Vol 96 (4) ◽  
pp. 251-257 ◽  
Author(s):  
T. Belytschko ◽  
A. H. Marchertas
Keyword(s):  
Finite Element ◽  
Dimensional Space ◽  
Equations Of Motion ◽  
Three Dimensional ◽  
Shell Element ◽  
Nonlinear Material ◽  
Time Step ◽  
Cross Sectional ◽  
Difference Formula ◽  
Lumped Masses

A finite-element procedure for transient analysis of plates and shells in three-dimensional space, and applicable to large displacements and nonlinear material properties, is described. This procedure employs a convected coordinate formulation enabling the use of simple strain-nodal displacement and nodal force-stress relations. The plate/shell element considers linear in-plane displacements and cubic transverse displacements. The orientation of lumped masses is described by unit vectors so that arbitrarily large rotations can be treated. Discretized equations of motion are integrated explicitly in time with a difference formula. Membrane artificial viscosity is utilized to stabilize occasional oscillations. The computational efficiency of the procedure is quite good: one element-time step takes 2 msec on an IBM 360/195 computer. Comparison of results with experimental data of impulsively loaded plates shows good agreement. The program was applied to a hexagonal fuel subassembly loaded internally. Various results are presented on its response and it is shown that, for that type of loading, two-dimensional cross-sectional models may be adequate.

Dynamic Modeling of a Flexible Manipulator With Prismatic Links

1999 ◽  
Vol 121 (4) ◽  
pp. 691-696 ◽  
Author(s):  
B. J. Torby ◽  
I. Kimura
Keyword(s):  
Moving Boundary ◽  
Dimensional Space ◽  
Equations Of Motion ◽  
Three Dimensional ◽  
Flexible Manipulator ◽  
Assumed Mode Method ◽  
Mode Method ◽  
Finite Element Node ◽  
Assumed Mode ◽  
Three Dimensional Space

In this paper the equations of motion for a flexible multi-link manipulator are derived. Each link of the manipulator, including those with prismatic motion, is represented by two finite elements in three-dimensional space. The prismatic links are treated as beams with moving boundary conditions, and the position of finite-element node points are not changed relative to the link. The equations are generated using Maple V, and the paper discusses a general approach for eliminating small terms. A sample calculation is performed for a RRP (Stanford arm) manipulator, and the shift of natural frequencies with time are plotted. Results are compared to those obtained by the assumed-mode method.

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