A finite element approach to the structural instability of beam columns, frames, and arches
Jerrell M. Thomas, United States. National Aeronautics and Space Administration, George C. Marshall Space Flight Center
National Aeronautics and Space Administration, 1970 - Mathematics - 48 pages
Stiffness matrix for structural stability analyses on beam columns, frames, and arches.
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6EI 6EI AIAA applied load behavior applied to element beam column element behavior stiffness matrix bifurcation theory Boeing Company Boundary conditions Column vector Conventional Stiffness Matrix Coordinate Transformation defined by equation deformed element Denotes a particular Derivation developed Discrete Element distributed load EA[u EA[w eigenvalue elastic stability element centerline element stiffness matrix Equation 46 equations 90 equilibrium equations example problem finite element method forces applied G matrix geometric stiffness matrix global coordinate system indicated by equation k,x j,x Lateral load LIST OF SYMBOLS load behavior stiffness loads remain directed Loads Remain Normal loads remain parallel lOL 10L magnitude Marshall Space Flight master stiffness matrix nodal displacements nodal forces obtained principle of virtual relationships set of equations shear strain energy Structural Analysis Structural Instability theory of elastic unconservative systems uniform circular arch vector of nodal virtual displacements xi zi XX dx xx xx xx zi xi