Force-based derivation of exact stiffness matrix for beams onWinkler-Pasternak foundation

2013 ◽  
Vol 95 (2) ◽  
pp. 140-155 ◽  
Author(s):  
Suchart Limkatanyu ◽  
Nattapong Damrongwiriyanupap ◽  
Minho Kwon ◽  
Paitoon Ponbunyanon
Keyword(s):  
Stiffness Matrix ◽  
Pasternak Foundation ◽  
Exact Stiffness Matrix

An Exact Three-Dimensional Beam Element With Nonuniform Cross Section

2010 ◽  
Vol 77 (6) ◽  
Author(s):  
M. Jafari ◽  
M. J. Mahjoob
Keyword(s):  
Cross Section ◽  
Stiffness Matrix ◽  
Degrees Of Freedom ◽  
Direct Method ◽  
Three Dimensional ◽  
Curved Beams ◽  
Element Analysis ◽  
Shear Loads ◽  
Line Passing ◽  
Exact Stiffness Matrix

In this paper, the exact stiffness matrix of curved beams with nonuniform cross section is derived using direct method. The considered element has two nodes and 12 degrees of freedom, with three forces and three moments applied at each node. The noncoincidence effect of shear center and center of area is also considered in this element. The deformations of the beam are due to bending, torsion, tensile, and shear loads. The line passing through center of area is a general three-dimensional curve and the cross section properties may change arbitrarily along it. The method is extended to deal with distributed loads on the curved beams. The stiffness matrix of some selected types of beams is determined by this method. The results are compared (where possible) with previously published results, simple beam finite element analysis and analytic solution. It is shown that the determined stiffness matrix is exact and that any type of beam can be analyzed by this method.

BUCKLING OF COLUMNS WITH INTERNAL SLIDE RELEASE

2002 ◽  
Vol 02 (04) ◽  
pp. 593-598 ◽  
Author(s):  
M. EISENBERGER ◽  
H. AMBARSUMIAN
Keyword(s):  
Stiffness Matrix ◽  
Buckling Load ◽  
Buckling Loads ◽  
Simply Supported ◽  
Axial Forces ◽  
Exact Stiffness Matrix

The exact buckling loads of columns with internal slide release are found using the exact stiffness matrix of the column including the effect of the axial forces. Two types of columns are considered: clamped–clamped and clamped-simply supported with internal slide release at variable locations along the member. It is found that for both the clamped–clamped and the clamped-simply supported columns the buckling load is constant and does not depend on the location of the slide discontinuity.

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