Large deflection analysis of curved beam problem with varying curvature and moving boundaries

The paper presents experimental and theoretical large deflection analysis of non-uniformly curved beam with moving boundaries under static loading within elastic domain. A master leaf spring is considered as physical model of the curved beam problem and its load-deflection behaviour is studied experimentally in a specially designed testing rig. Beside direct deflection measurement at some discrete points within the specimen domain, image processing technique is also used to obtain complete deflection profiles under loaded conditions. The indirect deflection measurement through post processing photographs of loaded master leaf is implemented manually in AutoCAD®. Deflection behaviour of the physical system involves strong geometric nonlinearity coming from non-uniform initial curvature, moving boundaries, nonlinear kinematics due to coupling between bending, stretching, shear deformation and large deflection, asymmetry in beam geometry and eccentricity in load application point with respect to geometric centre. All of these complicating effects are considered in the mathematical model of the physical system. As large deflection involves a large rigid body motion and the induced strain coming from deformation displacement is rather small, present analysis is carried out within elastic regime where material constitutive relation remains linear. Hence system governing equation is derived within the framework of geometric nonlinearity and small strain assumption, using energy principle based variational method. The nonlinear governing equation, in association with complicated moving boundary conditions, is solved iteratively through incremental loading using an updated Lagrangian approach. After each incremental load step, kinetic relation is also satisfied through shear force balance. Numerical results are generated for the same loading conditions of the experimental work and comparisons between theoretical and experimental results are quite good. However, the comparison study leads to identification of several geometric parameters of the physical system, incorporation of which may provide more realistic simulation.