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Compatibility condition in theory of solid mechanics (elasticity, structures, and design optimization)
| Content Provider | NASA Technical Reports Server (NTRS) |
|---|---|
| Author | Pai, Shantaram S. Patnaik, Surya N. Hopkins, Dale A. |
| Copyright Year | 2007 |
| Description | The strain formulation in elasticity and the compatibility condition in structural mechanics have neither been understood nor have they been utilized. This shortcoming prevented the formulation of a direct method to calculate stress. We have researched and understood the compatibility condition for linear problems in elasticity and in finite element analysis. This has lead to the completion of the method of force with stress (or stress resultant) as the primary unknown. The method in elasticity is referred to as the completed Beltrami-Michell formulation (CBMF), and it is the integrated force method (IFM) in structures. The dual integrated force method (IFMD) with displacement as the primary unknown has been formulated. IFM and IFMD produce identical responses. The variational derivation of the CBMF yielded the new boundary compatibility conditions. The CBMF can be used to solve stress, displacement, and mixed boundary value problems. The IFM in structures produced high-fidelity response even with a modest finite element model. The IFM has influenced structural design considerably. A fully utilized design method for strength and stiffness limitation has been developed. The singularity condition in optimization has been identified. The CBMF and IFM tensorial approaches are robust formulations because of simultaneous emphasis on the equilibrium equation and the compatibility condition. |
| File Size | 1992431 |
| Page Count | 42 |
| File Format | |
| Alternate Webpage(s) | http://archive.org/details/NASA_NTRS_Archive_20070021749 |
| Archival Resource Key | ark:/13960/t6n06421n |
| Language | English |
| Publisher Date | 2007-05-01 |
| Access Restriction | Open |
| Subject Keyword | Structural Mechanics Solid Mechanics Temperature Distribution Boundary Value Problems Mechanical Properties Equilibrium Equations Displacement Design Optimization Finite Element Method Structural Strain Michell Theorem Polar Coordinates Singularity Mathematics Mathematical Models Stiffness Elastic Properties Compatibility Loads Forces Ntrs Nasa Technical Reports Server (ntrs) Nasa Technical Reports Server Aerodynamics Aircraft Aerospace Engineering Aerospace Aeronautic Space Science |
| Content Type | Text |
| Resource Type | Technical Report |
