JOURNAL OF FACULTY OF CIVIL ENGINEERING 21, 2012.y., pp. 29-40GEOMETRICALLY NONLINEAR ANALYSIS OF PLANE BEAM STRUCTURES - PART II: EXAMPLES
|CC-BY-SA 4.0 license
|Author : Aleksandar Borković
|As shown in Part one, equations of statical equilibrium of Bernoulli-Euler
beam are derived according to von Karman theory. In this Paper elements of tangent
stiffness matrix and vector of unbalanced forces are given for beams of type k and g.
Standard procedure for derivation of this elements is numerical integration. By usage of
the built-in Wolfram Mathematica functions for symbolic integration, these elemens are
derived in closed-form. Presented procedure is validated through four numerical
examples by comparison with commercial FEM packages ABAQUS and SAP2000.
Classicalgeometricallynonlinear problems of plane beam structures are given: softening
and stiffening of construction as well as their cobination that takes place for shallow
arches. Boundary conditions and geometry are varied for better insight into presented
|Bernoulli-Eulerbeam, tangent stiffness matrix, vector of unbalanced forces,
beam of type k, beam of type g