Significance of Strain in Formulation in Theory of Solid Mechanics

By: Nasa, National Aeronautics and Space Adm

The basic theory of solid mechanics was deemed complete circa 1860 when St. Venant provided the strain formulation or the field compatibility condition. The strain formulation was incomplete. The missing portion has been formulated and identified as the boundary compatibility condition (BCC). The BCC, derived through a variational formulation, has been verified through integral theorem and solution of problems. The BCC, unlike the field counterpart, do not trivialize when expressed in displacements. Navier s method and the stiffness formulation have to account for the extra conditions especially at the inter-element boundaries in a finite element model. Completion of the strain formulation has led to the revival of the direct force calculation methods: the Integrated Force Method (IFM) and its dual (IFMD) for finite element analysis, and the completed Beltrami-Michell formulation (CBMF) in elasticity. The benefits from the new methods in elasticity, in finite element analysis, and in design optimization are discussed. Existing solutions and computer codes may have to be adjusted for the compliance of the new conditions. Complacency because the discipline is over a century old and computer codes have been developed for half a century can lead to stagnation of the discipline.Patnaik, Surya N. and Coroneos, Rula M. and Hopkins, Dale A.Glenn Research CenterMATHEMATICAL MODELS; SOLID MECHANICS; MECHANICAL PROPERTIES; STRUCTURAL STRAIN; BOUNDARY CONDITIONS; FINITE ELEMENT METHOD; MICHELL THEOREM; STRESS-STRAIN RELATIONSHIPS; NAVIER-STOKES EQUATION; STIFFNESS; BELTRAMI FLOW; STRAIN DISTRIBUTION; COMPUTER PROGRAMS

• Format: Paperback
• Language: English
• ISBN: 1723753882
• ISBN13: 9781723753886
• Release Date: January 1
• Publisher: Independently Published
• Length: 30 Pages
• Weight: 0.21 lbs.
• Dimensions: 0.1" x 8.5" x 11.0"