BOUSSINESQ PROBLEM OF PLANE MICROPOLAR ELASTICITY

A finite element formulation and solution is described of the boundary value problem of a concentrated force acting on a semi-infinite micropolar solid. In this work, which is based on the hypothesis that granular materials may be more accurately modelled by the theory of micropolar elasticity as opposed to classical elasticity, a stiffness matrix is derived for a flat micropolar rectangular elements in a plane state and use is made of this element to solve the case of the semi-infinite micropolar solid both in a state of plane stress and plane strain. The basic theory is set forth and details are given of the development of the stiffness matrix. The numerical results (presented and discussed) confirm the validity of the finite element model presented herein, provided that the body to be analyzed is divided into a sufficient number of elements. The results also indicate the lack of sensitivity of the quantities of interest, namely, the vertical stress and displacement, to one of the micropolar constants. Factors which effect the vertical stress and displacement are discussed. The finite element model described here may be used to solve several important practical problems of micropolar bodies in a state of plane stress or plane strain.

• Supplemental Notes:
  • Reprinted from International Journal for Numerical Methods in Engineering (London), Volume 8, 1974, pp 45-54.
• Corporate Authors:

  Purdue University

  Department of Civil Engineering, 550 Stadium Mall Drive
  West Lafayette, IN  United States  47907-2051
• Authors:
  • Korman, T
  • Goldberg, J E
  • Morghem, F
  • Baluch, M H
• Publication Date: 1974-7

Media Info

• Features: Figures; References; Tables;
• Pagination: 10 p.

Subject/Index Terms

• TRT Terms: Boundary value problems; Dislocation (Geology); Elasticity (Mechanics); Finite element method; Numerical analysis; Stiffness; Strain (Mechanics); Stresses
• Uncontrolled Terms: Boundary conditions; Plane strain; Vertical stress
• Old TRIS Terms: Boussinesq properties; Semi-infinite solids
• Subject Areas: Geotechnology; Highways;

Filing Info

• Accession Number: 00080920
• Record Type: Publication
• Report/Paper Numbers: CE 298
• Files: TRIS
• Created Date: Mar 6 1975 12:00AM