Geometric optimization of two bonded wedges involving stress singularities

✍ Scribed by Jungsun Park; W.J. Anderson

• Publisher: Elsevier Science
• Year: 1994
• Weight: 691 KB
• Volume: 4
• Category: Article
• ISSN: 0961-9526
• DOI: 10.1016/0961-9526(94)90034-5

✦ Synopsis

Joints between dissimilar materials can cause stress singularities. Such joints are exemplified by the case of two bonded wedges. The stress singularity can be avoided by reshaping the wedges. An analytical theory for the critical wedge angles of the bonded wedges is developed. The shape is optimized by the geometric strain method, an optimality criterion method. Numerical examples are presented for different materials with/without special conditions on the wedge angles. Optimum wedge shapes are obtained and optimum corner angles are compared with analytical wedge-angle solutions from contact mechanics. Both analytical and numerical approaches are useful tools for reshaping the bonded wedges to avoid a stress singularity.

NOMENCLATURE determinant of coefficients of system equation in contact mechanics

Mellin transform of a function g(r) shear modulus J-1 order of stress singularity real part of a complex number polar coordinates complex parameter displacement components Dundurs' parameters boundaries for exterior design, interior, traction and constrained regions lower and upper wedge angles critical wedge angle governing the presence of singularity Poisson's ratio variables in the complex plane Airy stress function stress components principal stresses region with applied body force, fully stressed domain imaginary part real part lower and upper wedges Mellin transform