Advanced Structural Mechanics
CE57000
Credit Hours:
3Learning 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: 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:
- 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:
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
Projects:
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
Exams:
Short quizzes 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
Textbooks (tentative):
Required:
KD Hjelmstad, Fundamentals of Structural Mechanics, Springer, 2005Computer 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
ProEd Minimum Requirements: