Nonlinear finite element analysis of composite beams and arches using a large rotation theory

Miller, Daniel A.; Palazotto, Anthony N.

doi:10.1016/0168-874x(95)00004-d

Cited by 15 publications

(7 citation statements)

References 9 publications

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“…Application of higher order beam theories in design of several Micro Electro-Mechanical system (MEMS), Nano Electro-Mechanical system (NEMS), carbon nanotubes, biosensors, micro actuators, nano probes, etc., have also been reported in some recent papers [31, 33, 34, 37, 46-52, 54-57, 59]. Several non-metallic materials offer high strength and low weight and hence modern trend in structural mechanics is to replace metallic structural elements by non-metallic ones, for example leaf springs [107,126], arches [103], micro and nano devices [31,55], etc., made of composite and functionally graded materials. Large deformation behavior of such non-metallic structures [67-70, 83, 91, 93, 96, 98, 103, 107, 114, 126] within elastic limits call for analysis in geometrical nonlinear setting.…”

Section: Application Areasmentioning

confidence: 99%

“…Energy based variational principle, such as principle of virtual displacement, minimization of total potential energy, etc. [58,[101][102][103][104], is mostly used to derive such element wise equation. However, force based formulation is also used [105].…”

Section: Numerical Methodmentioning

confidence: 99%

“…Many of beam like structures, like leaf springs [102,107], arches [92,95,103,110,112,122], etc., are not initially straight and undergo large amplitude transverse displacement during operation. They are generally analyzed by modeling them as initially curved beam.…”

Section: Initial Geometrymentioning

confidence: 99%

“…Two classical displacement based boundary conditions, used for stress and deflection analysis of beam, are fixed-free and simply supported. Many other boundary conditions, such as fixed-simply supported [61], clamped-clamped [59,91,96,98,110,119], hinged-clamped [92], simply supported-elastically restrained [16,76], hinged-hinged [103], stiffened lateral ends [68], are also prescribed for deflection analysis of beam structures. These different types of classical and nonconventional boundary conditions of beams are shown in Fig.…”

Section: Boundary Conditionmentioning

confidence: 99%

“…Most of the research works are performed on stress and deformation of beam like structures following geometric nonlinear theory for betterment of their design. Many researchers have reported these applications in automobile industry [102,107,126], aerospace application [104], designs of large displacement hinges in planar compliant mechanisms [73], arch [92,95,103,110,112,122] and adjustable stiffness spring [84], etc. One particular research paper reported stress analysis for simulation of sheet metal forming process [135].…”

Section: Application Areasmentioning

confidence: 99%

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

Ghuku

Saha

2017

IJET

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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.

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