Exact Analysis of Curved Beams and Arches with Arbitrary End Conditions: A Hamiltonian State Space Approach

Tarn, Jiann-Quo; Tseng, W.-D.

doi:10.1007/s10659-011-9335-4

Cited by 12 publications

(11 citation statements)

References 7 publications

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“…Generally, displacement kinematics is prescribed at boundaries, whereas force kinetics [93,95] is prescribed sometimes and mixed boundary condition arises rarely in some complicated beam bending problems [66,69,105,118]. Two classical displacement based boundary conditions, used for stress and deflection analysis of beam, are fixed-free and simply supported.…”

Section: Boundary Conditionmentioning

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%

“…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%

“…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.…”

mentioning

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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Section: Boundary Conditionmentioning

confidence: 99%

Section: Initial Geometrymentioning

confidence: 99%

Section: Application Areasmentioning

confidence: 99%

mentioning

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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“…But for concentrated force and other types of discontinuous loads, particular solutions can not be obtained directly in the present symplectic framework. Maybe further endeavors will be made to seek numerical solutions using numerical technique [30].…”

Section: Solutions For Homogenous Materialsmentioning

confidence: 99%

Analytical Solutions for Functionally Graded Beams under Arbitrary Distributed Loads via the Symplectic Approach

Zhao

Gan

2014

Advances in Mechanical Engineering

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A novel symplectic approach is employed in the analysis of homogenous and functionally graded beams subjected to arbitrary tractions on the lateral surfaces. Two models of functionally graded beams are heterogeneous in the sense that the material properties are exponential functions of the length and thickness, respectively. Within the symplectic framework, the method of separation of variables alone with the eigenfunction expansion technique is adopted to obtain the exact analysis of displacement and stress fields. The complete solutions include homogenous solutions with coefficients to be determined by two end boundary conditions and particular solutions satisfying the lateral boundary conditions. Two examples are presented for functionally graded beams to demonstrate the effects of material inhomogeneity. The efficiency and accuracy of the symplectic analysis are shown through numerical results.

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Impact toughness and wear resistance of different equivalent ratios of 316 L and 2Cr13 by laser melting deposition on Q235 steel

Zhao,

Huang,

Chen

et al. 2024

Materialwissenschaft Werkst

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This paper systematically studies cladding materials prepared by mixing 316 L and 2Cr13 alloy powders in different ratios. The powder was melted and deposited on a Q235B carbon steel substrate using laser melting deposition with a high Ni transition layer and appropriate laser process parameters. Bimetallic plates with a thickness of 10 mm ±0.5 mm was prepared. The microstructure of different parts of the bimetallic plates and the impact toughness and hardness were observed and tested under different alloy ratios. The results indicate that the Nickel‐Chromium equivalence ratio increased, the hardness and wear resistance of the bimetallic plates increased, and the degree of eutectic segregation in the eutectic structure also increased. When the ratio of 2Cr13 reached 60 %, the impact toughness increased significantly, and the needle‐like second phase appeared in the structure. X‐ray diffractometer analysis determined that this second phase was (Fe, Cr)7C3. After Charpy impact testing, the fracture microstructure showed many dimples, indicating micropore aggregation fracture. This study guides preparing large‐thickness cladding layers on iron and steel parts using laser melting deposition.

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Exact Analysis of Curved Beams and Arches with Arbitrary End Conditions: A Hamiltonian State Space Approach

Cited by 12 publications

References 7 publications

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

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

Analytical Solutions for Functionally Graded Beams under Arbitrary Distributed Loads via the Symplectic Approach

Impact toughness and wear resistance of different equivalent ratios of 316 L and 2Cr13 by laser melting deposition on Q235 steel

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