Modeling of the Beam Discontinuity with Two Analyses in Strong and Weak Forms using a Torsional Spring Model

Journal of Simulation and Analysis of Novel Technologies in Mechanical Engineering

مقاله 6، دوره 8، شماره 4، بهمن 2015، صفحه 295-309   

نوع مقاله: Persian

نویسندگان

M. Mastan Abadi¹؛ A. Alijani^{* 2}؛ A. Darvizeh³؛ F. Mottaghian⁴

¹MSc Student, Department of Mechanical Engineering, Takestan Branch, Islamic Azad University, Takestan, Iran

²Assistant Prof., Department of Mechanical Engineering, Bandar Anzali Branch, Islamic Azad University, Bandar Anzali, Iran

³Professor, Department of Mechanical Engineering, Bandar Anzali Branch, Islamic Azad University, Bandar Anzali, Iran

⁴MSc Student, Department of Mechanical Engineering, University of Guilan, Rasht, Iran

چکیده

In this paper, a discontinuity in beams whose intensity is adjusted by the spring stiffness factor is modeled using a torsional spring. Adapting two analyses in strong and weak forms for discontinuous beams, the improved governing differential equations and the modified stiffness matrix are derived respectively. In the strong form, two different solution methods have been presented to make an analogy between the formulation of the Euler-Bernoulli and Timoshenko theories that indicates the influence of the shear deformation in discontinuous beams. The flexural stiffness of discontinuous beams is corrected by using the Dirac’s delta function.  In the weak form, the reduced stiffness matrix is derived from the strain energy equation established by the continuity, kinematics and constitutive equations. The linearity assumption of the geometry and material is considered to construct the kinematics and constitutive equations respectively. The continuity conditions mathematically connect two divided parts of the Euler-Bernoulli beam for which an improved Hermitian shape function is employed to interpolate displacement field. An application shows the comparison and validation of the results of the strong and weak forms, and also the static behavior of discontinuous beams

کلیدواژه‌ها

Discontinuity؛ Beam؛ Strong and Weak Forms؛ Euler-Bernoulli؛ Timoshenko Theories

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