CADintegrated analysis of 3D beams: a surfaceintegration approach
 Wa’el Abdel Samad,
 Krishnan Suresh
 … show all 2 hide
Rent the article at a discount
Rent now* Final gross prices may vary according to local VAT.
Get AccessAbstract
Most engineering artifacts are designed and analyzed today within a 3D computer aided design (CAD) environment. However, slender objects such as beams are designed in a 3D environment, but analyzed using a 1D beamelement, since their 3D analysis exhibits locking and/or is computationally inefficient. This process is tedious and errorprone. Here, we propose a dualrepresentation strategy for designing and analyzing 3D beams, directly within a 3D CAD environment. The proposed method exploits classic 1D beam physics, but is implemented within a 3D CAD environment by appealing to the divergence theorem. Consequently, the proposed method is numerically and computationally equivalent to classic 1D beam analysis for uniform crosssection beams. But, more importantly, it closely matches the accuracy of a fullblown 3D finite element analysis for nonuniform beams.
 Requicha, AG (1980) Representations for rigid solids: theory, methods, and systems. ACM Comput Surv (CSUR) 12: pp. 437464 CrossRef
 Fu, MW, Ong, SK, Lu, WF, Lee, IBH, Nee, AYC (2003) An approach to identify design and manufacturing features from a data exchanged part model. Comput Aided Des 35: pp. 979993 CrossRef
 Pratt, MJ, Anderson, BD, Ranger, T (2005) Towards the standardized exchange of parameterized featurebased CAD models. Comput Aided Des 37: pp. 12511265 CrossRef
 Zienkiewicz, OC, Taylor, RL, Zhu, JZ (2005) The finite element method: its basis and fundamentals, 6th edn. Elsevier Butterworth Heinemann, Amsterdam
 Dow, J, Byrd, DE (1988) The Identification and elimination of artificial stiffening errors in finite elements. Int J Numer Methods Eng 26: pp. 743762 CrossRef
 Jog, CS (2005) A 27node hybrid brick and a 21node hybrid wedge element for structural analysis. Finite Elem Anal Des 41: pp. 12091232 CrossRef
 Duster, A, Broker, H, Rank, E (2001) The pversion of finite element method for threedimensional curved thin walled structures. Int J Numer Methods Eng 52: pp. 673703 CrossRef
 Braess, D, Kaltenbacher, M (2007) Efficient 3Dfiniteelementformulation for thin mechanical and piezoelectric structures. Int J Numer Methods Eng 73: pp. 147161 CrossRef
 Dorfmann, A, Nelson, RB (1995) Threedimensional finite element for analysing thin plate/shell structures. Int J Numer Methods Eng 38: pp. 34533482 CrossRef
 Jorabchi K, Danczyk J, Suresh K (2008) Algebraic reduction of beams for CADintegrated analysis. CAD (submitted)
 Wang, CM, Reddy, JN, Lee, KH (2000) Shear deformable beams and plates: relationship to classical solutions. Elsevier Science, London
 Pilkey, W (2002) Analysis and Design of Elastic Beams. Wiley, New York CrossRef
 Zhou, D, Cheung, YK (2001) Vibrations of tapered Timoshenko beams in terms of static Timoshenko beam elements. J Appl Mech 68: pp. 596603 CrossRef
 Lobontiu, N, Garcia, E (2004) Two microcantilever designs: lumpedparameter model for static and modal analysis. J Microelectromech Syst 13: pp. 4150 CrossRef
 Lu, ZR, Huang, M, Liu, JK, Chen, WH, Liao, WY (2009) Vibration analysis of multistepped beams with the composite element models. J Sound Vib 322: pp. 10701080 CrossRef
 Bronshtein, IN, Semendyayev, KA (1985) Handbook of mathematics. Van Nostrand Reinhold, New York
 Rathod, HT, Govinda Rao, HS (1998) Integration of trivariate polynomials over linear polyhedra in euclidean threedimensional space. J Aust Math Soc 39: pp. 355385 CrossRef
 Tessler, A, Dong, SB (1981) On a hierarchy of conforming Timoshenko beam elements. Comput Struct 14: pp. 335344 CrossRef
 SolidWorks (2005) SolidWorks. http://www.solidworks.com
 Zienkiewicz, OC, Taylor, RL (2005) The finite element method for solid and structural mechanics. Elsevier, Oxford
 Young, WC (1989) Roark’s formulas for stress and strain. McGraw Hill, New York
 Hsu, JC, Lee, HL, Chang, WJ (2007) Flexural vibration frequency of atomic force microscopy cantilevers using the Timoshenko beam model. Nanotechnology 18: pp. 285503 CrossRef
 Akinpelu, FO (2007) The effect of an attached mass on an EulerBernoulli beam. J Eng Appl Sci 2: pp. 12511254
 Title
 CADintegrated analysis of 3D beams: a surfaceintegration approach
 Journal

Engineering with Computers
Volume 27, Issue 3 , pp 201210
 Cover Date
 20110701
 DOI
 10.1007/s0036601001919
 Print ISSN
 01770667
 Online ISSN
 14355663
 Publisher
 SpringerVerlag
 Additional Links
 Topics
 Keywords

 Beams
 FEA
 Euler–Bernoulli
 Timoshenko
 Industry Sectors
 Authors

 Wa’el Abdel Samad ^{(1)}
 Krishnan Suresh ^{(1)}
 Author Affiliations

 1. 2059, Mechanical Engineering Building, University of Wisconsin, 1513 University Avenue, Madison, WI, 53706, USA