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.

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.

Nonlinear Theory for Flexural Motions of Thin Elastic Plate, Part 3: Numerical Evaluation of Boundary Layer Solutions

1982 ◽  
Vol 49 (2) ◽  
pp. 409-416
Author(s):  
N. Sugimoto
Keyword(s):  
Boundary Layer ◽  
Stress Singularity ◽  
Free Edge ◽  
Thin Elastic Plate ◽  
Normal Stresses ◽  
Interior Region ◽  
First Order ◽  
Plausible Values ◽  
Bending Stresses ◽  
Order Stress

The boundary layer solutions previoulsy obtained in Part 2 of this series for the cases of the built-in edge and the free edge are evaluated numerically. For the built-in edge, a characteristic penetration depth of the boundary layer toward the interior region is given by 0.13 εh, εh being the normalized thickness of the plate, while for the free edge, it is given by 0.32 εh. Thus the boundary layer for the free edge penetrates more deeply toward the interior region than that for the built-in edge. The first-order stress distribution in each boundary layer is displayed. For the built-in edge, the stress singularity appears on the edge. It is shown that, in the boundary layer, the shearing and normal stresses become comparable with the bending stresses. Similarly for the free edge, the shearing stress also becomes comparable with the twisting stress. It should be remarked that, in the boundary layer, the shearing or the normal stress plays a primarily important role as the bending or the twisting stress. But the former decays toward the interior region and remains higher order than the latter. Finally owing to these numerical results, the coefficients involved in the “reduced” boundary conditions for the built-in edge are evaluated for the various plausible values of Poisson’s ratio.

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.

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