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One-Dimensional Higher Order Elements

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Finite Elements Methods in Mechanics

Part of the book series: Solid Mechanics and Its Applications ((SMIA,volume 216))

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Abstract

The chapter begins with the definition of straight one-dimensional quadratic element, where the natural coordinate and the Jacobian matrix is then calculated. As an application, the field problem is selected and the stiffness and force matrices are calculated. The cubic element in the general and local coordinates are discussed the Jacobian of transformation is calculated. The layer-wise theory is then described and it is applied to a composite beam under static and dynamic loading conditions.

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References

  1. Stavsky Y (1963) Thermoelasticity of heterogeneous aelotropic plates. J Eng Mech Div ASCE 89:89–105

    Google Scholar 

  2. Nemirovskii YV (1972) On the theory of thermoelastic bending of reinforced shells and plates. Mech Compos Mat 8:579–750

    Google Scholar 

  3. Shaldyrvan VA (1980) Thermoelasticity problems for transversally isotropic plates. Sov Appl Mech 16:370–375

    Article  MATH  MathSciNet  Google Scholar 

  4. Rao MNB (1979) Three dimensional analysis of thermally loaded thick plates. Nuclear Eng and Des 55:353–361

    Article  Google Scholar 

  5. Wu CH, Tauchert TR (1980) Thermoelastic analysis of laminated plates, part 1: symmetric specially orthotropic laminates. J Thermal Stresses 3:247–259

    Article  Google Scholar 

  6. Wu CH, Tauchert TR (1980) Thermoelastic analysis of laminated plates, part 2: antisymmetric cross-ply and angle-ply laminates. J Thermal Stresses 3:365–378

    Article  Google Scholar 

  7. Khadeir AA, Reddy JN (1991) Thermal stress and deflection of cross-ply laminated plates using refined plate theories. J Thermal Stresses 14:419–438

    Article  Google Scholar 

  8. Huang NN, Tauchert TR (1991) Thermoelastic solution for cross-ply cylindrical panels. J Thermal Stresses 14:227–237

    Article  Google Scholar 

  9. Huang NN, Tauchert TR (1991) Thermal stresses in doubly-curved cross-ply laminates. Int J Solids and Structures 29:991–1000

    Article  Google Scholar 

  10. Thanjitham S, Choi HJ (1991) Thermal stresses in a multilayered anisotropic medium. J Appl Mech 58:1021–1027

    Article  Google Scholar 

  11. Noor AK, Burthon WS (1992) Computational models for high temperature multilayered composite plates and shells. Appl Mech Rev 45:419–446

    Article  Google Scholar 

  12. Tanigawa Y, Murakami H, Ootao Y (1989) Transient thermal stress analysis of laminated composite beam. J Thermal Stresses 12:25–39

    Article  Google Scholar 

  13. Tanigawa Y, Ootao Y, Murakami H (1991) Thermal bending of laminated composite rectangular plates and nonhomogeneous plates due to partial heating. J Thermal Stresses 14:285–308

    Article  Google Scholar 

  14. Chen D, Cheng S, Gerhart TD (1982) Thermal stresses in laminated beams. J Thermal Stresses 5:67–74

    Article  Google Scholar 

  15. Cho KN, Stirz AG, Bert CW (1989) Thermal stress analysis of laminate using higher-order theory in each layer. J Thermal Stresses 12:321–332

    Article  Google Scholar 

  16. Eslami MR, Naghdi AY, and Shiari B (1996) Static analysis of thermal stresses in beams based on layer-wise theory. In: Proceedings of the 1st National Aerospace and Aeronautics Conference Amirkabir University of Technology .

    Google Scholar 

  17. Eslami MR, Naghdi AY, Shiari B (1997) Dynamic analysis of thermal stresses in beams based on layer-wise theory. In: Proceedings of the ISME Nat Conf, Tabriz University

    Google Scholar 

  18. Jones RM (1975) Mechanics of composite materials. McGraw-Hill, New York

    Google Scholar 

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Correspondence to M. Reza Eslami .

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Eslami, M.R. (2014). One-Dimensional Higher Order Elements. In: Finite Elements Methods in Mechanics. Solid Mechanics and Its Applications, vol 216. Springer, Cham. https://doi.org/10.1007/978-3-319-08037-6_14

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  • DOI: https://doi.org/10.1007/978-3-319-08037-6_14

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-08036-9

  • Online ISBN: 978-3-319-08037-6

  • eBook Packages: EngineeringEngineering (R0)

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