Advanced Structural Mechanics


Credit Hours:


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: Compute approximate solutions to problems in structural mechanics


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
  6. Energy Methods and Variational principles: Directional derivative; Vainberg's theorem
  7. Numerical solutions to boundary value problems: Ritz method; Introduction to the Finite element method
  8. Structural mechanics of beams: Kinematic hypothesis; Stress resultants; Planar beam: Timoshenko & Bernoulli-Euler formulations
  9. Structural mechanics of plates: Kinematic hypothesis; Stress resultants 

Web Address:


Web Content:

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


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 


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 


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):


KD Hjelmstad, Fundamentals of Structural Mechanics, Springer, 2005
(PDF available through Purdue Libraries

Computer Requirements:


Obtain and run MATLAB at Purdue: 

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

ProEd Minimum Requirements: