vanderbilt university civil and environmental engineering department

                            Semester:   Instructor:    

Class  Hours:   Venue:   Textbooks:  

VANDERBILT    UNIVERSITY     CIVIL    AND    ENVIRONMENTAL    ENGINEERING    DEPARTMENT   Course:  CE  301  –  Advanced  Mechanics  of  Solids  I   Fall  2013     Ravindra  Duddu   Office  –  274  Jacobs  Hall   Telephone  –  (615)  343  4891   E-­‐mail  –  [email protected]   My  office  hours  are  flexible,  so  please  send  me  an  email.     M,  W    (1:10  to  2:25pm)     FGH  200     1. Introduction  to  the  Continuum  Mechanics,  by  M.  W.  Lai,   D.  Rubin,  E.  Krempl,  Elsevier,  2010.       2. Advanced  Mechanics  of  Materials,  by  A.  P.  Boresi  and  R.  J.   Schmidt  Fenster,  Sixth  Edition,  John  Wiley  &  Sons,  2003.       3. Elasticity  –  Theory,  Applications  and  Numerics,  by  M.  H.   Saad,  Elsevier,  2009.       (The  above  two  are  available  as  e-­‐books  online  through   the  Knovel  system  via  Vanderbilt  Library)  

  Tentative  Syllabus     1. Introduction  and  Notation     1.1. The  continuous  media  assumption   1.2. Scalars,  vectors  and  tensors   1.3. Indicial,  tensor  and  matrix  notation   1.4. Scalar,  vector  and  tensor  products   1.5. Change  of  orthonormal  basis    (rotation  of  axis)   1.6. Principal  values  and  principal  directions   1.7. Cylindrical  coordinates     2. Stress,  strain  and  deformation    

2.1. Traction  and  stress  tensor   2.2. Principal  values  of  stress  tensor,  volumetric  and  deviatoric  stress   2.3. Motion  and  deformation,  current  and  reference  configurations   2.4. Geometric  measures  of  deformation   2.5. Strain  measures,  linearized  displacement  gradients   2.6. Stress  measures  and  conjugates     3. Linear  and  nonlinear  elasticity       3.1. Linearized  elasticity,  material  symmetry  and  Lamé  constants   3.2. Restrictions  on  elastic  constants   3.3. Linearized  theory  of  elasticity   3.4. Mathematical  theory  of  elasticity     3.5. Polar  coordinates  and  examples  problems     4. Fracture  Mechanics     4.1. Introduction:  mode  I,  II  and  III  fracture   4.2. Energy  approach  to  brittle  fracture   4.3. Stress  intensity  factors   4.4. Mode  I  stress  intensity  factor  solutions   4.5. Fracture  process  zone  and  the  limitations  of  linear  elastic  fracture  mechanics     Grading Homework

30%

Midterm I

15%

Midterm II

15%

Final quiz

30%

Term paper

10%

  Homework     Homework  will  be  mostly  theoretical  and  the  students  are  required  to  turn  them  in  neat   handwriting.  Alternatively,  homeworks  may  be  typed  in  MS  Word  or  Latex.  Submission   of  the  homework  is  typically  2  weeks  after  it  has  been  assigned.  MATLAB  programming   may  be  a  part  of  the  assignments  and  students  are  required  to  email  the  working  codes.     Midterms  and  Final  quiz       The  exams  are  usually  closed  book,  however,  2  pages    of  cheat  sheets  can  be  used  to   write  down  formulas  related  to  tensor  and  vector  calculus.  Calculators  are  allowed.    

Term  paper     The  students  will  be  allowed  to  choose  a  complex  theoretical  or  computational  problem   and  will  be  required  to  submit  upto  a  5  page  report  proving  either  solutions  or  results.   Computational  problems  may  solved  using  ANSYS,  ABAQUS  or  MATLAB.  It  is  strongly   recommended  that  students  consult  with  me  about  their  project.  The  term  paper  will  be   due  on  the  last  class  day  of  the  semester.       Other  reference  books:     1. Gurtin,  M.E.,  “An  Introduction  to  Continuum  Mechanics,”  Academic  Press.     2. Malvern,  L.  E.,  “Introduction  to  the  Mechanics  of  a  Continuous  Medium,”  Prentice-­‐ Hall,  1969.     3. Gonzalez,  O.  and  Stuart,  A.M.,  “A  First  Course  in  Continuum  Mechanics,”  Cambridge   University  Press.       4. Timoshenko.  S.P.  and  Goodier,  J.N.,  "Theory  of  Elasticity,"    McGraw-­‐Hill  Book  Co.       5. Pook,  L.P.,  “Linear  Elastic  Fracture  Mechanics  for  Engineers:  Theory  and   Applications,”  Computational  Mechanics  Inc.       6. Love,  A.E.H.,  “A  Treatise  on  the  Mathematical  Theory  of  Elasticity,”  Dover     7. Sokolnikoff,  I.S.,  “Mathematical  Theory  of  Elasticity,”  McGraw-­‐Hill     8. Boresi,  A.P.  and    Chong,  K.P.,  “  Elasticity  in  Engineering  Mechanics,”  Elsevier     9. Filonenko-­‐Borodich,  M.,  “Theory  of  Elasticity,”    Foreign  Language  Publishing  House,   Moscow     10. Fung,  Y.C.,  “Foundations  of  Elasticity,  “  Prentice-­‐Hall     11. Mall,  A.K.  and  Singh,  S.,  “Deformation  of  Elastic  Solids,”  Prentice-­‐Hall     12. Mushkelisvilli,  N.I.,  “Some  Basic  Problems  of  the  Mathematical  Theory  of  Elasticity,”   Noordhoff     13. Scada,  “Elasticity  -­‐  Theory  and  Applications,”  Pergamon  Press     14. Wang,    C.    ,  “Applied  Elasticity,”  McGraw-­‐Hill