# ENGRMAE 157 Lightweight Structures (2011-2012)

#### ENGRMAE 157 Lightweight Structures

**ENGRMAE 157 Lightweight Structures (Credit Units: 4)** Fundamentals of torsion and bending. Analysis and design of thin-wall and composite beams. Stress analysis of aircraft components. Stiffness, strength, and buckling. Introduction to the Finite Element method and its application to plates and shells. Prerequisite: MAE150 or CEE150 or ENGR150. (Design units: 2)

- T.H.G. Megson, Aircraft Structures for Engineering Students, 4th Ed., Butterworth-Heinemann, 2007.
- CT Sun, Mechanics of Aircraft Structures, Wiley, 1998.
- HD Curtis, Fundamentals of Aircraft Structural Analysis, McGraw-Hill, 1997.

1. Calculate the stress distribution in one-dimensional structural elements under any combination of axial, bending, shear and torsional loads. (EAC a, EAC-9 ME-2)

2. Calculate the maximum design loads that a structure can tolerate, using the appropriate failure criteria for yielding and buckling. (EAC a, EAC c, EAC e)

3. Appreciate the concepts of statical determinacy and indeterminacy (EAC a)

4. Understand the approximations involved in the structural idealization of aircraft components. (EAC e, EAC k)

5. Design minimum-weight structures subject to multiple requirements (strength, stiffness, size, etc…). (EAC c)

6. Understand the main concepts of elastic buckling, and appreciate that lightweight structures are subject to multiple buckling modes (e.g. local VS global buckling). (EAC a, EAC c, EAC-9 ME-2)

7. Learn the fundamentals of the Finite Element method, and develop a working knowledge of a commercial package for the static analysis of lightweight structures (including eigenvalue analysis for the prediction of the critical buckling loads). (EAC a, EAC i, EAC k, EAC-9 ME-3)

8. Solve structural problems using applied engineering mathematical concepts – calculus, trigonometry, linear (matrix) algebra, differential equations, coordinates transformation. (EAC a, EAC e, EAC-9 ME-2, EAC-9 ME-3)

9. Work in a team environment, by participating in a design project culminating in written report and oral presentation (EAC c, EAC d, EAC e, EAC i, EAC k)

Statics of solid bodies. Analysis of structures. Mechanics of materials. Stress and strain.

- Introduction to aircraft construction. The objective of minimum weight and lightweight structures: examples from aircraft design
- Advanced strength of materials applied to one-dimensional elements:
- Torsion: Shear stress distribution in thin-walled shafts
- Bending: Normal stress distribution for non-symmetric sections
- Bending: Shear stress distribution in thin-walled beams

- Introduction to continuum structures from a statical determinacy standpoint. Summary of 2D elasticity: plane stress/strain, principal stresses/strains, Mohr’s circle
- Failure criteria: yielding (Von Mises, Tresca) and buckling
- Introduction to the Finite Element method for elastic continua
- Finite elements description (and solution) of plates and shells (with ABAQUS)

Meets for 3 hours of lecture and 1 hour of discussion each week for 10 weeks.

A commercial programming language (e.g. MATLAB) will be used to optimize the dimensions of a minimum-weight structure under realistic design constraints. In addition, students will learn how to use a commercial Finite Element code (e.g. ABAQUS, or MSC.Nastran) for the structural analysis of more complex lightweight structures.

Contributes toward the Mechanical Engineering Topics courses and Major design experience. Contributes toward the Aerospace Engineering Topics courses and Major design experience.

A team-oriented design project is aimed at the optimization and accurate analysis of a minimum-weight structure subject to a number of realistic loads and constraints. A light-weight structure that meets ideal design criteria (i.e. mass, deflection, strength, etc.) is to be designed by groups of four or more students. Two full lectures are devoted to the design project. Topics to be covered are: problem definition, design variables, design constraints, the optimization procedure, and interpretation of results. In the second half of the quarter, all discussion sessions supplement and office hours give first priority to the team-oriented design project. Students have full access to structural analysis software during both sessions.

- Problem Sets: 20%
- Design Project: 15%
- Midterm Exam: 30%
- Final Exam: 35%
- Total: 100%

Mathematics and Basic Science: 0.0 credit units

Computing: 0.0 credit units

Engineering Topics: 4.0 credit units

Engineering Science: 2.0 credit units

Engineering Design: 2.0 credit units