Static task of von Mises planar truss analyzed using the potential energy
Abstract
A Von Mises planar truss subjected to vertical static load at its top joint is studied. The mathematical concept of large displacement elastic analysis of the von Mises truss targeted for computers is described. The model geometry is described using finite mass points. Formulae for the evaluation of displacements of mass points and rotation of segments were derived with the help of geometrical and physical conditions. Formulae for the determination of potential energy of the system are listed. Deformation of the structure is evaluated by seeking the minimal potential energy. The stepbystep increment method combined with NewtonRaphson method is used. The mathematical solution described in the article enables the modelling of Mises truss using a finite amount of segments. The described solution is suitable for loaddeflection curve computation of a limit load model. The equilibrium stability problem of von Mises truss is discussed in connection with the random effects of imperfections.
 Publication:

11th International Conference of Numerical Analysis and Applied Mathematics 2013: ICNAAM 2013
 Pub Date:
 October 2013
 DOI:
 10.1063/1.4825952
 Bibcode:
 2013AIPC.1558.2107K