CAD-integrated analysis of 3-D beams: a surface-integration approach
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Most engineering artifacts are designed and analyzed today within a 3-D computer aided design (CAD) environment. However, slender objects such as beams are designed in a 3-D environment, but analyzed using a 1-D beam-element, since their 3-D analysis exhibits locking and/or is computationally inefficient. This process is tedious and error-prone. Here, we propose a dual-representation strategy for designing and analyzing 3-D beams, directly within a 3-D CAD environment. The proposed method exploits classic 1-D beam physics, but is implemented within a 3-D CAD environment by appealing to the divergence theorem. Consequently, the proposed method is numerically and computationally equivalent to classic 1-D beam analysis for uniform cross-section beams. But, more importantly, it closely matches the accuracy of a full-blown 3-D finite element analysis for non-uniform beams.
KeywordsBeams FEA Euler–Bernoulli Timoshenko
The authors wish to acknowledge the support of the National Science Foundation under grants OCI-0636206, and CMMI-0726635, CMMI-0745398.
- 4.Zienkiewicz OC, Taylor RL, Zhu JZ (2005) The finite element method: its basis and fundamentals, 6th edn. Elsevier Butterworth Heinemann, AmsterdamGoogle Scholar
- 10.Jorabchi K, Danczyk J, Suresh K (2008) Algebraic reduction of beams for CAD-integrated analysis. CAD (submitted)Google Scholar
- 11.Wang CM, Reddy JN, Lee KH (2000) Shear deformable beams and plates: relationship to classical solutions. Elsevier Science, LondonGoogle Scholar
- 16.Bronshtein IN, Semendyayev KA (1985) Handbook of mathematics. Van Nostrand Reinhold, New YorkGoogle Scholar
- 19.SolidWorks (2005) SolidWorks. http://www.solidworks.com
- 21.Young WC (1989) Roark’s formulas for stress and strain. McGraw Hill, New YorkGoogle Scholar
- 23.Akinpelu FO (2007) The effect of an attached mass on an Euler-Bernoulli beam. J Eng Appl Sci 2:1251–1254Google Scholar