A Hybrid Finite Element Approach to Composite Laminate Elasticity Problems With Singularities

1983 ◽  
Vol 50 (4a) ◽  
pp. 835-844 ◽  
Author(s):  
S. S. Wang ◽  
F. G. Yuan
Keyword(s):  
Finite Element ◽  
Composite Laminates ◽  
Composite Laminate ◽  
Stress Singularity ◽  
Free Edge ◽  
Anisotropic Elasticity ◽  
Hybrid Finite Element Method ◽  
Hybrid Finite Element ◽  
Elasticity Problems ◽  
Basic Equations

A hybrid finite element method is presented for studying composite laminate elasticity problems with singularities. The basic equations of laminate anisotropic elasticity and stress singularities in composite laminates are discussed briefly. Formulation of a singular, hybrid composite-wedge element for this class of problems is given in detail. Two numerical examples are shown to illustrate the accuracy and efficiency of the present method of approach. The first example is the well-known laminate free-edge problem, which has a rather weak stress singularity; the second one is the important composite problem, which is shown to have a strong stress singularity. Results are compared with existing analytical elasticity solutions for these problems. Excellent solution accuracy, convergence, and computational efficiency are demonstrated.

Boundary Element Solution for Free Edge Stresses in Composite Laminates

1997 ◽  
Vol 64 (4) ◽  
pp. 877-884 ◽  
Author(s):  
G. Davi` ◽  
A. Milazzo
Keyword(s):  
Boundary Element ◽  
Composite Laminates ◽  
Stress Singularity ◽  
Free Edge ◽  
Fundamental Solutions ◽  
Boundary Integral ◽  
Elastic Response ◽  
Stress Problem ◽  
Edge Stress ◽  
Basic Equations

The edge-stress problem in multilayered composite laminates under uniform axial extension is analyzed through an alternative method based on a boundary integral formulation. The basic equations of the formulation are discussed and solved by the multiregion boundary element method. Generalized orthotropic elasticity analytic fundamental solutions are employed to establish the integral equations governing the problem. The formulation is absolutely general with regard to the laminate stacking sequence and the section geometry and it does not require any aprioristic assumption on the elastic response nature. This makes the formulation suitable for an investigation of the singular behavior of the stress field at the free edge in composite laminates. The interlaminar normal and shear stress distributions are examined in detail with the aim of calculating the stress singularity at the interlaminar free edge. The singularity parameters, i.e., power and strength, are determined for two family of laminates in order to ascertain the effectiveness of the method for the free edge-stress problem.

Boundary-Layer Effects in Composite Laminates: Part 1—Free-Edge Stress Singularities

1982 ◽  
Vol 49 (3) ◽  
pp. 541-548 ◽  
Author(s):  
S. S. Wang ◽  
I. Choi
Keyword(s):  
Boundary Layer ◽  
Composite Laminates ◽  
Stress Singularity ◽  
Homogeneous Solution ◽  
Expansion Method ◽  
Free Edge ◽  
Anisotropic Elasticity ◽  
Stress Singularities ◽  
Eigenfunction Expansion Method ◽  
Reinforced Composite

A study of boundary-layer stress singularities in multilayered fiber-reinforced composite laminates is presented. Based on Lekhnitskii’s stress potentials and the theory of anisotropic elasticity, formulation of the problem leads to a pair of coupled governing partial differential equations (P.D.E.’s). An eigenfunction expansion method is developed to obtain the homogeneous solution for the governing P.D.E. ’s. The order or strength of boundary-layer stress singularity is determined by solving the transcendental characteristic equation obtained from the homogeneous solution for the problem. Numerical examples of the singular strength (or singular eigenvalues) of boundary-layer stresses are given for angle-ply and cross-ply composites as well as the cases of more general composite lamination.

scholarly journals Modelling Plates and Shells by Means of the Rigid Finite Element Method

2015 ◽  
Vol 62 (1) ◽  
pp. 101-114 ◽  
Author(s):  
Iwona Adamiec-Wójcik ◽  
Andrzej Nowak ◽  
Stanisław Wojciech
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Free Vibrations ◽  
The Finite Element Method ◽  
Hybrid Finite Element Method ◽  
Hybrid Finite Element ◽  
Rigid Finite Element Method ◽  
Plates And Shells ◽  
Single Set ◽  
Element Method

Abstract The rigid finite element method (RFEM) has been used mainly for modelling systems with beam-like links. This paper deals with modelling of a single set of electrodes consisting of an upper beam with electrodes, which are shells with complicated shapes, and an anvil beam. Discretisation of the whole system, both the beams and the electrodes, is carried out by means of the rigid finite element method. The results of calculations concerned with free vibrations of the plates are compared with those obtained from a commercial package of the finite element method (FEM), while forced vibrations of the set of electrodes are compared with those obtained by means of the hybrid finite element method (HFEM) and experimental measurements obtained on a special test stand.

Dynamic Analysis of Marine Risers With Vortex Excitation

1982 ◽  
Vol 104 (1) ◽  
pp. 14-19 ◽  
Author(s):  
R. P. Nordgren
Keyword(s):  
Finite Element Method ◽  
Time Integration ◽  
Elastic Rods ◽  
Hybrid Finite Element Method ◽  
Marine Risers ◽  
Hybrid Finite Element ◽  
Wake Oscillator ◽  
Transverse Vibrations ◽  
Basic Equations ◽  
Oscillator Equations

The basic equations for nonplanar transverse vibrations of marine risers are derived from the theory of elastic rods. A numerical method is developed for solution of the equations by time integration. Spatial discretization is accomplished by a hybrid finite element method. Vortex excitation is modeled by the coupled wake oscillator proposed by Iwan and Blevins. The vortex oscillator equations are integrated numerically in time along with the riser equations. By way of example, several typical riser problems are analyzed including forced vibration and vortex-induced vibration.

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