Improved Displacement-Field Approximation for Geometrical Nonlinear Flexibility-Based Planar Curved Element in State Space^#

^#Communicated by S. Cho.

Abstract

This research is to offer a higher-order approximation method for a planar curved beam with enhanced formulation accuracy in state space. Here, the differential equations along with algebraic ones are formed and solved simultaneously, having no problem with element state determinations. The flexibility-based method, in which force interpolation functions are used, forms the basis of this technique. The presented field studied in this research originates from two existing techniques: curvature-based displacement interpolation, used in matrix-based flexibility formulations, and linear displacement approximation applied in state space. In order to develop the higher-order field, the Reissner's strains are approximated by Lagrange polynomials. This field offers responses with higher accuracy using fewer elements and integration points in comparison with other force-based and displacement-based methods. Focusing on the accuracy and regarding the performed analyses, it seems that the computational cost is reduced in a wide range of engineering problems.

Keywords:

• Displacement-field approximation
• Force-based method
• Geometrical nonlinearity
• State space approach

Notes

^#Communicated by S. Cho.