End effects for plane deformations of an elastic anisotropic semi-infinite strip. Final report

Thesis/Dissertation · Sun May 01 04:00:00 EDT 1994

OSTI ID:574926

Miller, K L

In the linear theory of elasticity, Saint-Venant`s principle is used to justify the neglect of edge effects when determining stresses in a body. For isotropic materials, the validity of this is well established. However for anisotropic materials, experimental results have shown that edge effects may persist much farther into the material than for isotropic materials and as a result cannot be neglected. This research examines the effect of material anisotropy on the exponential decay rate for stresses in a semi-infinite elastic strip. A linear elastic semi-infinite strip in a state of plane stress/strain subject to a self-equilibrated end load is considered first for a specially orthotropic material and then for the general anisotropic material. The problem is governed by a fourth-order elliptic partial differential equation with constant coefficients. Conservation properties of the solution are derived to help to determine a stress decay rate estimate. Energy methods are then used to establish lower bounds on the actual stress decay rate. Both analytic and numerical estimates are obtained in terms of the elastic constants of the material and results are shown for several contemporary engineering materials. When compared with the exact stress decay rate computed numerically from the eigenvalues of a fourth-order ordinary differential equation, the results in some cases show a high degree of accuracy. Results of the type obtained here have several important practical applications.

• Research Organization: Air Force Research Lab., Bolling AFB, Washington, DC (United States)
• OSTI ID: 574926
• Report Number(s): AD-A--334929/7/XAB; AFRL-SR-BL-TR--98-0021
• Country of Publication: United States
• Language: English

Related Subjects

36 MATERIALS SCIENCE
ANISOTROPY
COMPOSITE MATERIALS
DEFORMATION
ELASTICITY
END EFFECTS
NUMERICAL ANALYSIS
STRESS RELAXATION
STRESSES