Advanced Structural Mechanics - CE57000
Studies of stress and strain, failure theories, and yield criteria; flexure and torsion theories for solid and thin-walled members; and energy methods.
Credit Hours: 3
Instructor(s): Arun Prakash
Email: aprakash@purdue.edu
Office: HAMP 4119
Web: Instructor Homepage
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
Topics Covered:
- Introduction and Mathematical Preliminaries: Mechanics of solids/structures; Vector algebra; Tensors and matrices; Vector and tensor calculus
- Kinematics of deformation: Deformation map and deformation gradient, rotation and stretch; Strain and physical significance; compatibility
- Stress and equilibrium of deformable bodies: Free body diagrams; Traction and stress; Equilibrium and balance principles; First and second Piola-Kirchhoff stresses
- Material models: Material frame indifference; objectivity; Hyperelasticity; Isotropy; Hooke's model
- 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
- Numerical solutions to boundary value problems: Ritz method; Introduction to the Finite element method
- Structural mechanics of beams: Kinematic hypothesis; Stress resultants; Planar beam: Timoshenko & Bernoulli-Euler formulations
- Structural mechanics of plates: Kinematic hypothesis; Stress resultants
Web Address: https://purdue.brightspace.com
Web Content: Syllabus, grades, lecture notes, homework assignments, solutions and quizzes
Homework: Every week, 3 homework problems will be assigned - due in 2 parts:
- Part 1: Due by Saturday of the week; Solution posted immediately after due date
- Part 2: Correct errors and make comments - due by Saturday of the following week Late submissions will not be accepted (unless approved by the instructor in advance).
Projects: During Weeks 1-10: Individual student-led MATLAB project - due in 2 phases:
- Phase 1: Students will complete the project, prepare slides, record a short video presenting their project, and submit on Circuit - due by Sunday of the week
- Phase 2: Students conduct a peer evaluation of 3 of their peers and a self evaluation on Circuit - due by Saturday of the following week
Exams: Every week, take an online quiz based on the assigned Reading and Videos, Maximum 2 attempts - higher score recorded. Due by Saturday of the week. 4 Live quizzes: Held on Thursdays of Weeks 3, 6, 9, and 12. Online students should attend live on Zoom during class time (if possible) or contact the instructor to schedule an alternative 30-minute time-slot in the same week.
Textbooks: Required: KD Hjelmstad, Fundamentals of Structural Mechanics, Springer, 2005 (PDF available through Purdue Libraries)
Computer Requirements: 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