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G.D. Ramtekkar

Bio: G.D. Ramtekkar is an academic researcher from National Institute of Technology, Raipur. The author has contributed to research in topics: Plate theory & Bending of plates. The author has an hindex of 6, co-authored 6 publications receiving 189 citations.

Papers
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Journal ArticleDOI
TL;DR: An analytical model for free vibration and geometrically linear thermal buckling phenomenon of a thin rectangular isotropic plate containing a continuous line surface or internal crack located at the centre of the plate using classical plate theory is proposed in this article.
Abstract: An analytical model is proposed for free vibration and geometrically linear thermal buckling phenomenon of a thin rectangular isotropic plate containing a continuous line surface or internal crack located at the centre of the plate using classical plate theory. The crack terms are formulated using Line Spring Model. The in-plane forces are due to the uniform heating of the cracked plate. Applying the Galerkin׳s method, the equation is transformed into Duffing equation which shows the effect of uniform rise in temperature on natural frequencies. A classical relation for buckling temperature for a cracked plate is also determined.

44 citations

Journal ArticleDOI
TL;DR: In this paper, an analytical model for nonlinear vibrations in a cracked rectangular isotropic plate containing a single and two perpendicular internal cracks located at the center of the plate is proposed.

43 citations

Journal ArticleDOI
TL;DR: In this paper, an analytical model for vibration analysis of a thin orthotropic and general functionally graded rectangular plate containing an internal crack located at the center is presented, where the continuous line crack is parallel to one of the edges of the plate.

40 citations

Journal ArticleDOI
TL;DR: In this paper, a non-classical analytical model is presented for free vibration of the cracked rectangular isotropic and functionally graded micro plates in the presence of thermal environment, where the crack terms are based on the Line Spring Model whereas the thermal environment is accommodated in the form of thermal moment and inplane forces.

39 citations

Journal ArticleDOI
TL;DR: In this paper, an analytical model is presented for vibration analysis of a thin orthotropic plate containing a partial crack located at the centre of the plate. And the effect of varying elasticity ratio on fundamental frequency of cracked plate is also established.
Abstract: An analytical model is presented for vibration analysis of a thin orthotropic plate containing a partial crack located at the centre of the plate. The continuous line crack is parallel to one of the edges of the plate. The equation of motion of an orthotropic plate is derived using the equilibrium principle based on Classical Plate Theory. The crack terms are formulated using the Line Spring Model. Using Berger's formulation for the in-plane forces and Galerkin's method for solution, the derived equation involving a cubic nonlinear term is converted into the Duffing equation. The effect of nonlinearity is established by deriving the frequency response equation for the cracked plate using the method of multiple scales. The influence of crack length and boundary conditions on the fundamental frequency of square and rectangular plate is demonstrated for three boundary conditions. It is found that the vibration characteristics are affected by the presence of crack. Further, it is deduced that the presence of a crack across the fibres affects the fundamental frequency more as compared to a crack along the fibres. The effect of varying elasticity ratio on fundamental frequency of cracked plate is also established.

37 citations


Cited by
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Journal ArticleDOI
TL;DR: The present plate theory approach accounts for both transverse shear and normal deformations and satisfies the zero traction boundary conditions on the surfaces of the plate without using shear correction factor.
Abstract: This work presents an efficient and original high-order shear and normal deformation theory for the static and free vibration analysis of functionally graded plates. The Hamilton’s principle is used herein to derive the equations of motion. The number of unknowns and governing equations of the present theory is reduced, and hence makes it simple to use. The present plate theory approach accounts for both transverse shear and normal deformations and satisfies the zero traction boundary conditions on the surfaces of the plate without using shear correction factor. Unlike any other theory, the number of unknown functions involved in displacement field is only four, as against five or more in the case of other shear and normal deformation theories. The accuracy of the proposed solution is checked by comparing it with other closed form solutions available in the literature.

100 citations

Journal ArticleDOI
TL;DR: In this paper, a critical review of works reported in this area with an objective of providing the key challenges and future scopes of development in the direction of analysis of such structure for assessing safety in the presence of cracks.
Abstract: Performances of conventional fiber reinforced composites are challenged in thermomechanical loading, when development of interlaminar stresses at the interface becomes the weakest link of the components. Development of functionally graded materials (FGMs) could lead to the reduction of such interlaminar failures, especially at high temperature applications. Therefore, these FGMs have a huge potential for use in many structural applications, particularly under thermomechanical loading. There has been a large number of works already reported on FGM components, starting from manufacturing to stress analysis of such components. Cracks in such FGM components may develop due to variety of reasons during service and need to be addressed while analyzing the performances of such components. This paper reviews the progress made till date on the analysis of structural components made of FGMs with a special emphasis on the analysis of cracked FGM components. In view of the potential use of components made of FGMs in a wide range of applications, it is important to understand the state of the art in this area. This paper thus provides a critical review of works reported in this area with an objective of providing the key challenges and future scopes of development in the direction of analysis of such structure for assessing safety in the presence of cracks.

72 citations

Journal ArticleDOI
TL;DR: Comparisons show that XIGA-Jaya performs the best of all considered techniques, and is demonstrated by using various NURBS orders to reduce the number of elements, provide fast simulation and achieve best convergence compared with XFEM.

67 citations

Journal ArticleDOI
TL;DR: In this paper, the authors present an overview of the existing literature on stability, buckling, and free vibration analysis of FGM carried out by numerous authors in the past decade, and the analyses of mathematical models adopted for the aforementioned analyses are not the core purpose of this paper.
Abstract: Functionally graded materials (FGMs) are novel materials whose properties change gradually with respect to their dimensions. It is the advanced development of formerly used composite materials and consists of two or more materials in order to achieve the desired properties according to the application where an FGM is used. FGMs have obtained a great attention of researchers in the past decade due to their graded properties at every single point in various dimensions. The properties of an FGM are not identical to the materials that constitute it. This paper aims to present an overview of the existing literature on stability, buckling, and free vibration analysis of FGM carried out by numerous authors in the past decade. Moreover, the analyses of mathematical models adopted for the aforementioned analyses are not the core purpose of this paper. At the end, future work is also suggested in this review paper.

63 citations

Journal ArticleDOI
TL;DR: In this article, the authors proposed an analytical model for vibration analysis of partially cracked rectangular plates coupled with fluid medium, where the influence of surrounding fluid medium is incorporated in the governing equation in the form of inertia effects based on velocity potential function and Bernoulli's equations.

54 citations