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CE 595: Finite Elements in Elasticity

Page 1
Spring 2013
CE 595: Finite Elements in Elasticity
School of Civil Engineering Purdue University
1 Instructor: E-mail: Office Hours: Arun Prakash arunprakash@purdue.edu 4119, Civil Engineering building Mondays & Fridays 2:30-4:30pm; Or email for an appointment. Class Webpage:
http://www.itap.purdue.edu/tlt/blackboard
Lecture Time and Location: M-W-F 1:30pm-2:20pm, FRNY-G124 Course Description: Fundamentals of theory of elasticity; variational principles; one-, two-, and three-dimensional elasticity finite elements; interpolation methods; numerical integration; convergence criteria; stress interpretation. (See the list of topics for details). Prerequisite: CE-474 Structural Analysis II (or equivalent) Recommended Prerequisite: CE-570 Advanced Structural Mechanics (or equivalent) Vector Calculus, Solid and Structural Mechanics Computer Programming (MATLAB) Students will be expected to complete programming assignments in MATLAB and gain some experience with Finite element software programs such ABAQUS, ANSYS, LS-DYNA etc. The choice of software is up to the student. ote: ABAQUS student version is available FREE at the following link:
http://campus.3ds.com/simulia/FreeSE/
Grading Basis: • Homeworks 30% • Midterm - 1 20% • Midterm - 2 20% • Final Exam 30% • Total 100% Bonus 5% 6:30pm – 7:30pm, Mon February 18, Location MSEE B-012. 6:30pm – 7:30pm, Mon March 25, Location MSEE B-012. To be announced. For in-class activities, online forum participation Students should notify the instructor about conflicts with the scheduled exams allowing sufficient time to verify the conflict and arrange an alternate time. Make-up exams for absences will not be given except under extremely unavoidable situations. Academic Integrity • All work (assignments and exams) that you submit must be strictly your own work. • Obtaining solutions from another student or from any other external source (and/or letting others copy from you) is absolutely not allowed. Collaboration in the form of giving and receiving help on concepts is allowed and encouraged. Emergency Procedures In the event of a major campus emergency, course requirements, deadlines and grading percentages are subject to changes that may be necessitated by a revised semester calendar or other circumstances. Information regarding these changes will be posted on the course webpage and you will be intimated using the class email list.

Page 2
Spring 2013
CE 595: Finite Elements in Elasticity
School of Civil Engineering Purdue University
2 List of Topics: • Introduction to problems in Structural Engineering, Finite Element History (Ref: Reddy Ch 1, Z&T Vol 1 Ch 1) • Basic Review of Solid/Structural Mechanics / Theory of Elasticity (Ref: Hjelmstad Ch 1-4; Timoshenko & Goodier) - Concept of Cauchy stress, Equilibrium, Notation: using coordinates; indices; vectors & tensors - Deformation, Strains, Compatibility, Hyper-elasticity • 1D Boundary Value Problem (Ref: Hjelmstad Ch5, 6; Reddy Ch 2, 3; Hughes Ch 1) - Governing Differential Equation (Strong Form) - Principle of Virtual Work (Weak form), Method of weighted residuals, Raleigh-Ritz - Energy method, Variational Approach (Alternative Weak form), Calculus of Variations - Finite Element Discretization (Galerkin Form), Notation - 1D Quadrature, Equation solving, Boundary Conditions - 1-D FE Code structure (MATLAB) - Applications • 2D & 3D Problems (Ref: Reddy Ch 8, 9, 11; Hughes Ch 2; Z&T Vol 1 Ch 2, 3, 4, 5) - Strong Form, Weak form, Integral Theorems, Principle of Virtual Work, - Finite Element – CST, Q4, Voight notation, Calculation of edge loads, - 2D Quadrature, Area coordinates - Iso-parametric formulation, Jacobian, Element Quality - Boundary conditions & Constraints - Finite Element Families: Lagrange, Serendipity - Locking, Reduced Integration, Non-conforming modes - Convergence requirements, Patch Tests, - Post-processing, Stress recovery, Superconvergence, Error estimates - Axi-symmetric problems - 3D finite elements - Finite Deformation, Newton-Raphson - Dynamics: Hamilton��s Principle, Euler Lagrange Equations, (Ref: Hughes Ch8, 9) - Discretization: Mass & Damping matrices, Time-stepping • Beams & Frames (Ref: Hjelmstad Ch7; Reddy Ch5; Z&T Vol 2 Ch 10) - Bernoulli-Euler, Timoshenko - Hermite-cubic C1 shape functions - 3D Frame structures • Plates & Shells (Ref: Hjelmstad Ch 8; Reddy Ch 12; Hughes Ch 5, 6; Z&T Vol 2 Ch 11 & 12) - Kirchhoff-Love, - Reissner-Mindlin • Advanced Topics (if time permits) - Material Models – J2 Plasticity - Mixed Forms, Hu-Washizu, Hellinger-Reissner, LBB condition

Page 3
Spring 2013
CE 595: Finite Elements in Elasticity
School of Civil Engineering Purdue University
3 Text Books (required): • JN Reddy, An introduction to the Finite Element method, 3rd Edition, McGraw Hill • KD Hjelmstad, Fundamentals of Structural Mechanics, Springer. (Available FREE through Purdue Libraries) Text Books (recommended): • O.C. Zienkiewicz and R.L. Taylor, The Finite Element Method, Volumes I, II & III, 6th Edition Butterworth & Hinemann publishers. (Available FREE through Purdue Libraries) • TJR Hughes, The Finite Element Method, Dover Publication.

Page 4
Spring 2013
CE 595: Finite Elements in Elasticity
School of Civil Engineering Purdue University
4 Other Text Books • J. Fish and T. Belytschko, A first course in Finite Elements, Wiley & Sons. (ABAQUS student edition - Free CD) • R.D. Cook, D.S. Malkus, M.E. Plesha and R.J. Witt, Concepts & Applications of Finite Element Analysis, 4th Edition, Wiley & Sons. • R.D. Cook, Finite Element Modeling for Stress Analysis, Wiley & Sons. • K.J. Bathe, Finite Element Procedures. Prentice Hall. • D. Logan, A first course in Finite Element Method, Fourth Edition, Thomson Publishers. • T.R. Chandrupatla and A. Belegundu, Introduction to Finite Elements in Engineering, Prentice Hall. FEM for onlinear Problems • J. Bonet and R. D. Wood. onlinear continuum mechanics for finite element analysis. Cambridge University Press, Cambridge, UK, 1997. • T. Belytschko, W. K. Liu, and B. Moran. onlinear Finite Elements for Continua and Structures. John Wiley & Sons, 2000. • J. T. Oden. Finite Elements of onlinear Continua. Dover Publications, 2006. Mathematical Theory of Finite Elements • B. Szab�� and I. Babuska. Finite Element Analysis. John Wiley & Sons, 1991. • P. G. Ciarlet. The Finite Element Method for Elliptic Problems. SIAM, 2002. • G. Strang and G.J. Fix. An Analysis of the Finite Element Method, Wellesley-Cambridge. • D. Braess, Finite Elements, Cambridge. • S. C. Brenner and L. R. Scott. The Mathematical Theory of Finite Element Methods. Springer, 1994. and many more ��
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