Accession Number : AD0846250

Title :   Numerical Methods for the Nonlinear Analysis of an Elastic Arch,

Corporate Author : ARMY MISSILE COMMAND REDSTONE ARSENAL AL SYSTEMS RESEARCH DIRECTORATE

Personal Author(s) : Patrick, Grady E., Jr

Report Date : DEC 1968

Pagination or Media Count : 52

Abstract : In a recent paper, Wempner presented a method by which the finite deflections of thin shells are approximated in finite elements and the nonlinear differential equations are replaced by nonlinear algebraic equations. This is accomplished by decomposing the motion of an element into a rigid-body rotation and a deformation. The deformation of a Hookean element is characterized by linear constitutive equations relating generalized forces and small relative displacements. Nonlinearities arise from the differences in the rigid-body rotations of adjacent elements. In the present paper, the method is applied to formulate algebraic equations for the finite deflections of a circular arch. The constitutive equations of the finite element are the exact linear equations of the Winkler-Bach theory. The nonlinear algebraic equations are replaced by a succession of linear equations, each governing the response to a small increment of load. To eliminate cumulative error, the numerical results are inserted in the nonlinear equations and corrected by the Newton-Raphson procedure. (Author)

Descriptors :   (*SHELLS(STRUCTURAL FORMS), LOADS(FORCES)), NUMERICAL ANALYSIS, NONLINEAR DIFFERENTIAL EQUATIONS, DEFLECTION, DEFORMATION, RINGS, CONTINUUM MECHANICS, NONLINEAR SYSTEMS, ALGEBRAS.

Subject Categories : Structural Engineering and Building Technology
      Mechanics

Distribution Statement : APPROVED FOR PUBLIC RELEASE