Large Displacement of Crossbeam Structure through Energy Method

Abstract

This paper undertakes a geometric nonlinear large displacement static analysis of crossbeam structure. A crossbeam structure comprises two beams in contact with their longitudinal axes perpendicular to each other, used effectively in civil and mechanical engineering, marine and aerospace structures. The energy method forms the basis for the mathematical formulation and the governing set of equations are obtained using the principle of extremisation of the total energy of the system in its equilibrium state. To obtain the solution, an iterative procedure is developed based on the reaction force generated between the two beams of the system. The method is validated by experiment and simulation through ANSYS v11. Results are presented in terms of plots of reaction force and the displacement of the interaction point versus load in dimensional form and additionally, the deflected shapes of the crossbeam structure at static equilibrium condition, under a particular load, are provided. The static response of the system has been studied for variation of beam thickness, loading pattern and position of the supporting beam.

A Review on Stress and Deformation Analysis of Curved Beams under Large Deflection

“…Large displacement of initially curved beam induces a stretching effect and provides additional stiffening to the structures. The beam curvature leads to a coupling between the displacement fields coming from bending and stretching which leads the analysis of system response in the field of geometric nonlinearity [97,118]. Moreover, non-prismatic beam geometry [71,80,90,91] adds complexity in the analysis.…”

“…Usually deflection is measured with respect to its initial undeformed configuration. Conventional displacement measurement techniques include tensile testing machine [126], Hopkinson pressure bar [108], contact type [65,73,97] and non-contact type [84] displacement sensors, vernier height gauge [118], rulers [106,118], vernier caliper and dial caliper [109], electronic device like LVDT [59], etc. Several displacement measurement methods based on image processing technique are being extensively used nowadays [75,118].…”

“…Advantage of this approach is that it can undertake nonlinear curvature-slope and nonlinear stress-strain relations easily [92,93]. Principle of minimization of total potential energy [94][95][96][97][98] is a generalization for deformable elastic bodies of the total potential energy of particles and rigid bodies. Mathematically the principle is represented as 0 ) (    , where  is the variational operator and  is the total potential energy of the system.…”

“…Firstly, unknown displacement field is assumed satisfying boundary conditions through several approximate methods such as Ritz method, Galerkin method, etc. Then the assumed displacement field is substituted in energy equation, resulting in residual error of the system, minimization of which provides desired solution [94,97,98].…”

Effect of Particle Size and Packing Ratio of PID on Vibration Amplitude of Beam

“…The metal box provided the highest loss factor, but it was accompanied by a high noise level and great sensitivity to the amount of clearance given to the particles. The response of the hard plastic bag was largely insensitive to gap size (Cempel & Lotz, 1993;Mitra, Sahoo, & Saha, 2012). Sensitivity to clearance was also investigated while studying different combinations of particle sizes.…”