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Biswas, Arup Kumar
- Introduction to Finte Element Method
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Authors
Affiliations
1 Dept. of Mechanical Engineering, Kalyani Govt. Engineering College, Kalyani, IN
1 Dept. of Mechanical Engineering, Kalyani Govt. Engineering College, Kalyani, IN
Source
Journal of the Association of Engineers, India, Vol 83, No 3-4 (2013), Pagination: 84-84Abstract
This book is exclusievely designed for the beginners who would deal with finite element method (FEM). The book has been written in simple, lucid and easily understandalde fashion. The author has used his long teaching experience of the subject and derived FEM formulation in his own way, in a slightly different approach from the available books on FEM. There are fourteen well-organised chapters, and four appendices on Matrix algebra, Solution of equation, Numerical integration and Rayleigh-Ritz method. The appendices are quite useful for learners. However, the book has few limitations. The author has not discussed FEM formulation for Fluid Mechanics and Heat Transfer problems. This is understandably due to the fact that the focus of the book is mainly stress analysis of different types of structural problems. Functional and Galerkin's apprach have also not been discussed in the book. Despite this, the book will be very essential for learners, and can be highly recommended to the students who take FEM as subject in undergraduate and post graduation level. Another feature of this publication is web-basd availability of demo programme and help file which would benefit learners.
- Micro-indentation of a Conical Rigid Wedge by Numerical Slip-line Field Theory: A Hybrid Approach
Abstract Views :384 |
PDF Views:3
Authors
Affiliations
1 Mechanical Engineering Department, Kalyani Government Engineering College, Kalyani-741235, West Bengal, IN
2 Mechanical Engineering Department, Kalyani Government Engineering College, Kalyani -741235, West Bengal, IN
3 Department of Engineering and Technological Studies, Kalyani University, Kalyani-741235, West Bengal, IN
1 Mechanical Engineering Department, Kalyani Government Engineering College, Kalyani-741235, West Bengal, IN
2 Mechanical Engineering Department, Kalyani Government Engineering College, Kalyani -741235, West Bengal, IN
3 Department of Engineering and Technological Studies, Kalyani University, Kalyani-741235, West Bengal, IN
Source
Indian Science Cruiser, Vol 31, No 3 (2017), Pagination: 36-42Abstract
Slip-line field theory is generally applied for determination of plastic flow lines, stress, velocity of flow and plastic work. In this work, micro-indentation of a conical wedge into an infinitely long block has been analysed by numerical simulation of slip-line field equations. Though the previous works in this field considered straight line profile of the bulged material around the wedge, experimental results showed that the free surface of the material is not actually straight but curvilinear in shape. This work computes the slip line field considering the free surface separately as linear, or parabolic, or circular in nature. The combinations of linear and parabolic as well as linear and circular profiles are also studied. Results obtained in this work indicate suitability of the method showing good matching with the results reported in published literature.Keywords
Surface Profile, Micro-indentation, Slip-line Field, Numerical Technique, Hybrid Analysis.References
- R Hill, E H Lee and S J Tupper, The Theory of Wedge Indentation of Ductile Materials, Proceedings of Royale Society of London A, Vol 188, No.1013, page 273-289, 1947.
- J Grunzweig, I M Longman and N J Petch, Calculations and Measurements on WedgeIndentation, Journal Mechanics and Physics of Solids, Vol 2, page 81-86, 1954.
- R. Hill, On the Limits Set by Plastic Yielding to the Intensity of Singularities of Stress, Journal Mech. Phys. of Solids, Vol 2, page 278285, 1954.
- J B Haddow and H T Danyluc, Indentation of a Rigid-Plastic Semi-Infinite Media, by a Smooth Rigid Cone Fitted in a Prepared Cavity, Int. Journal of Mechanical Sciences, Vol 6, page 1-11, 1964.
- J B Haddow, On a Plane Strain Wedge Indentation Paradox, Int. Journal of Mechanical Sciences, Vol 9, No.4, page 159161, 1967.
- B Dodd and K Osakada, A Note on the Types of Slip-Line Field for Wedge Indentation Determined by Computer, Int. Journal of Mechanical Sciences, Vol 16, page 931-938, 1974.
- Y Bai and B Dodd, A Slip-Line Field Solution for Pale-Strain Indentation by Obtuse Angle Wedge, Int. Journal of Mechanical Sciences, Vol 24, page 119-123, 1982.
- N Ogasawara, N Chiba and X Chen, Limit Analysis-Based Approach to Determine the Material Plastic Properties with Conical Indentation, J. Mater. Res., Vol 21, No.10, page 2699-2700, 2006.
- T O Muliearn, The Deformation of Metals by Vickers-Type Pyramidal Indenters, J. Mech. Phys. Solids, Vol 7, page 85-96, 1959.
- A K Biswas, S Das, B Das and S Das, A SlipLine Field Solution for Micro-Indentation of a Rigid Conical Wedge by Numerical Technique, Int. Journal of Innovative Research in Science, Engineering and Technology, Vol 4, page 9094, 2015.
- J M Challen and P L B Oxley, Slip-Line Fields for Explaining the Mechanics of Polishing and Related Processes, Int. J. Mechanical Sciences, Vol 26, No.6-8, page 403-418, 1984.
- J M Challen and P L B Oxley, An Explanation of the Different Regimes of Friction and Wear Asperity Deformation Models, Wear, Vol 53, page 229-243, 1979.
- J M Challen, P L B Oxley and B S Hockenhull, Prediction of Archard’s Wear Co-Efficient for Metallic Sliding Friction Assuming a Low Cycle Fatigue Wear Mechanism, Wear, Vol 111, page 275-288, 1986.
- Y Yang and A A Torrance, Wear by Plastic Ratchetting: An Experimental Investigation, Wear, Vol 196, page 147-155, 1996.
- Y Yang, A A Torrance and P L B Oxley, Modelling Mechanical Wear Process in Metallic Sliding Friction, J. of Physics D. App. Phys., Vol 29, page 600-608, 1996.
- M. Busquet and A. Torrance, A Numerical Slip Line Field for Sliding Cylinder Problem, Wear, Vol 241, page 86-98, 2000.
- Bibliography
- R Hill, The Mathematical Theory of Plasticity, Oxford University Press, 1950.
- J Chakraborty, Theory of Plasticity, Elsevier Pub, 4th Edition, 2006.
- Introduction of a Non-Linear Shape Function to One Dimensional Two Noded Element in Finite Element Analysis : A Novel Approach
Abstract Views :132 |
PDF Views:1
Authors
Affiliations
1 Department of Mechanical Engineering, Kalyani Government Engineering College, Kalyani-741235, West Bengal, IN
1 Department of Mechanical Engineering, Kalyani Government Engineering College, Kalyani-741235, West Bengal, IN
Source
Indian Science Cruiser, Vol 36, No 6 (2022), Pagination: 51-54Abstract
Conventionally, linear shape functions are used for two noded one dimensional elements. Determination of coefficients of a second degree polynomial are restricted to one dimensional two noded element as it requires more than two boundary conditions at each node. The present work introduces a new nonlinear trigonometric shape function to a one dimensional two noded element. Results with newly introduced shape function show better matching with exact solution to the specified solid mechanics problem.Keywords
Non-Linear Shape Function, One Dimensional Element, Two Noded Element, Finite Element Analysis, FEM.References
- J N Reddy, An Introduction to Finite Element Method, McGraw Hill, New York (Int. Ed.), 1985.
- T R Chandrupatla and A D Belegundu, Introduction to Finite Elements in Engineering, PHI Publication (India), 1999.
- O C Zienkiewicz and R L Taylor, Finite Element Method, 4th Edition, McGraw Hill (UK), London, Vol 1, page 150-181, 1989.
- R L Taylor, On Completeness of Shape Functions for Finite Element Analysis, Int. J. Numer. Methods, Vol 4, No 1, page 17-22, 1972.
- S Chakrabarti, Trigonometric Function Representation for Rectangular Plate Bending Elements, Int. J. Numer. Methods, Vol 3, No 2, page 261-273, 1971.
- M A Eisenberg and L E Malvern, On Finite Element Integration in Natural Coordinates, Int. J. Numer. Methods, Vol 7, page 574-575, 1973.