A parametric study on geometrically nonlinear behavior of curved beams with single and double link rods, and supported on moving boundary

Abstract

The paper presents a parametric study on effect of several geometric parameters on stress and deformation behavior of non-uniform curved beam with moving boundary. The parameters, considered in the present study, are height to span ratio of curved beam, ratio of radius of roller support to height of beam and types of support connection mechanisms. Effect of these parameters is observed for different curved profile shapes. Non-uniform initial curvature and combined effects of bending, stretching and warping of beam cross-section due to shear deformation are considered in the derivation of nonlinear strain-displacement relation in body fitted curvilinear frame. Based on the derived nonlinear kinematics and assumptions of large deformation but small strain and moderate initial curvature, nonlinear system governing equation is derived through variational principle based minimization of total potential energy method. An iterative numerical solution algorithm is developed and implemented in the computational environment of MATLAB® software to solve the nonlinear governing equation. The complicating effect coming from moving boundary imposes a kinematic constraint on the solution field. Hence, the solution methodology not only ensures energy balance of the system, but also satisfies shear force balance at each incremental load step. The geometric nonlinear incremental curved beam model is validated with deflection and stress results of commercial finite element software ABAQUS®. The geometry of master leaf spring of a previously reported study is considered as curved beam for the purpose of validation. After the validation study, results are generated for different curved profiles with two different combinations of support connection mechanisms and different height to span ratio for each type of them. In addition, to observe effect of roller radius, results are generated with different roller radius to height ratio for each type of the two curved beam systems. Investigations are made on the effects of the geometric parameters, support connection mechanisms and curved profile shape on large deflection characteristics of curved beam and the present study leads towards several meaningful observations.