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

Abstract

Abstract. The paper presents a review on large deflection behavior of curved beams, as manifested through the responses under static loading. The term large deflection behavior refers to the inherent nonlinearity present in the analysis of such beam system response. The analysis leads to the field of geometric nonlinearity, in which equation of equilibrium is generally written in deformed configuration. Hence, the domain of large deflection analysis treats beam of any initial configuration as curved beam. The term curved designates the geometry of center line of beam, distinguishing it from the usual straight or circular arc configuration. Different methods adopted by researchers, to analyze large deflection behavior of beam bending, have been taken into consideration. The methods have been categorized based on their application in various formats of problems. The nonlinear response of a beam under static loading is also a function of different parameters of the particular problem. These include boundary condition, loading pattern, initial geometry of the beam, etc. In addition, another class of nonlinearity is commonly encountered in structural analysis, which is associated with nonlinear stress-strain relations and known as material nonlinearity. However the present paper mainly focuses on geometric nonlinear analysis of beam, and analysis associated with nonlinear material behavior is covered briefly as it belongs to another class of study. Research works on bifurcation instability and vibration responses of curved beams under large deflection is also excluded from the scope of the present review paper.

Theoretical analysis and a parametric study on forced vibration of large statically deformed curved beam with rigid links and moving support

“…7 The present work addresses three major research areas, namely, large static deformation, free vibration, and forced vibration of curved beams. Foundation theories for large static deformation analysis of curved beams along with several analysis methods are well documented in the papers, 8,9 and hence are not discussed here to maintain brevity. The foundation of large amplitude vibration of generalized beams along with several aspects of forced vibration characteristics of curved beams together with frequently encountered complicating effects due to non-classical parameters are discussed in the following paragraphs.…”

Stiffness analysis of leaf spring system under large deformation

“…31,33,34 As detailed review on such research works is out of scope of the present paper, interested readers may refer to the papers. 35,36…”

Free vibration analysis of large deformed curved beam incorporating rotary inertia and shear deformation effects and its experimental validation

“…As focus of the present work is on loaded vibration of large statically deformed curved beam, scope of the present literature review includes two different aspects: large deflection analysis of curved beam under static loading and free vibration problem of such beams. Detailed review of static large deflection curved beam problem is previously reported in the review paper, 7 and hence, only the second aspects of the problem are presented here to maintain brevity.…”