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 2—Free-Edge Stress Solutions and Basic Characteristics

1982 ◽  
Vol 49 (3) ◽  
pp. 549-560 ◽  
Author(s):  
S. S. Wang ◽  
I. Choi
Keyword(s):  
Boundary Layer ◽  
Composite Laminates ◽  
Failure Modes ◽  
Numerical Solutions ◽  
Complete Solution ◽  
Stress Singularity ◽  
Fracture Initiation ◽  
Free Edge ◽  
Boundary Region ◽  
Edge Stress

Boundary-layer effects in composite laminates are considered. Based on the theory of anisotropic elasticity and Lekhnitskii’s complex-variable stress function formulation, the exact laminate elasticity solution is derived for the problem. The solution contains the exact boundary-layer stress singularity and higher-order terms in eigenfunction series. Convergence and accuracy of the solution are studied, and present results are compared with existing approximate numerical solutions. For illustrative purposes, the complete solution for a symmetric [45/−45 / −45/45] graphite-epoxy composite is presented to elucidate fundamental characteristics of the boundary-layer effects. Detailed stress distributions in the boundary-layer region are determined. Boundary-layer stress intensity factors are introduced to characterize the singular edge-stress field. Physical significance of the parameters is discussed in the realm of fracture initiation and failure modes in the laminate boundary region.

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.

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