Advanced Structural Mechanics

CE 57000

Credit Hours:

3

Instructor:

Dr. Arun Prakash

Learning Objective:

Upon completion of the course, students will be able to:

CLO1: Comprehend and utilize mathematical tools to describe problems in structural mechanics
CLO2: Develop mathematical descriptions of deformation of structures
CLO3: Evaluate the state of stress in structural components under different loading conditions
CLO4: Construct relationships between stress and strain for different materials
CLO5: Compute approximate solutions to problems in structural mechanics

Description:

Studies of stress and strain, failure theories, and yield criteria; flexure and torsion theories for solid and thin-walled members; and energy methods

Topics Covered:

  1. Introduction and Mathematical Preliminaries: Mechanics of solids/structures; Vector algebra; Tensors and matrices; Vector and tensor calculus
  2. Kinematics of deformation: Deformation map and deformation gradient, rotation and stretch; Strain and physical significance; compatibility;
  3. Stress and equilibrium of deformable bodies: Free body diagrams; Traction and stress; Equilibrium and balance principles; First and second Piola-Kirchhoff stresses
  4. Material models: Material frame indifference; objectivity; Hyperelasticity; Isotropy; Hooke’s model
  5. Boundary value problems in solid mechanics: Strong and Weak forms, 1D problems; 2D Plane stress/strain, examples; 3D strong forms and solution methods, examples; Principle of virtual work
    Energy Methods and Variational principles: Directional derivative; Vainberg’s theorem
  6. Numerical solutions to boundary value problems: Ritz method; Introduction to the Finite element method
  7. Structural mechanics of beams: Kinematic hypothesis; Stress resultants; Planar beam:Timoshenko & Bernoulli-Euler formulations
  8. Structural mechanics of plates: Kinematic hypothesis; Stress resultants

Web Address:

https://purdue.brightspace.com/d2l/login

Web Content:

Syllabus, grades, lecture notes, homework assignments, solutions and quizzes

Assignments:

Students will need to complete the following assignments every week:

  • Reading - Review posted slides and corresponding sections from the textbook
  • Videos - Review assigned videos for the week
  • Quiz - Take a short quiz based on the Reading and Videos – maximum 3 attempts
    • Quiz attempt 1 due by Tuesday of the week
    • Quiz attempts 2 and 3 due by the end of the week
  • Homework - 3 homework problems assigned on Monday of each week – due in 2 parts:
    • Part-1: Due by Friday of the week; Solution posted immediately after due date
    • Part-2: Correct errors and make comments – due by Friday of the following week
    • Late submissions will NOT be evaluated.
  • Project: Individual student-led computing projects assigned each week – due in 2 phases:
    • Phase 1: Student completes the project, prepares slides and records a short video presenting their project – due by Saturday of the week
    • Phase 2: Students conduct a peer evaluation of 3 of their peers on Circuit tool in addition to instructor evaluation – due by Saturday of the following week
    • Late submissions will NOT be evaluated.

Grading Scale:

Student scores will be weighted as follows:

Quizzes 20%

Homeworks 30%

Projects 40%

Quiz/Interview 10% (In-class quiz on Friday, Dec-9 OR Zoom interview during Dec-5 to Dec-9)

Total 100%

Final grade will be assigned based on the total score in accordance with the following ranges*:

A+ / A / A- > 90%

B+ / B / B- 80% - 90%

C+ / C / C- 70% - 80%

D 60% - 70%

F < 60%

* These ranges may be revised up or down at the sole discretion of the instructor.

Textbooks:

Official textbook information is now listed in the Schedule of Classes. NOTE: Textbook information is subject to be changed at any time at the discretion of the faculty member. If you have questions or concerns please contact the academic department.

Tentative Textbook Listing:

Required Textbook:

KD Hjelmstad, Fundamentals of Structural Mechanics, Springer, 2005.

(PDF available through Purdue Libraries)

Required Software: MATLAB

Obtain and run MATLAB at Purdue:

https://engineering.purdue.edu/ECN/Support/KB/Docs/MatlabToolboxes

Complete a 2-hour self-paced crash course (called MATLAB Onramp) at:

https://www.mathworks.com/help/matlab/getting-started-with-matlab.html