MEEN4004W Vehicle Structural Analysis

Academic Year 2024/2025

This module introduces the basics of Continuum Mechanics, and Finite Volume (FV) and Finite Element (FE) methods, to demonstrate how fundamental laws of Physics can be turned into powerful numerical tools. This theoretical basis and knowledge is then applied to practical applications of FV and FE methods in vehicle structural analysis. This pertains to the sequential progression of coursework from the foundational solid mechanics modules presented in the second-year course MEEN2003W to the advanced concepts explored in the third-year course MEEN3002W.

1. Basic concepts and definitions: Concept of continuum; Continuity, Homogeneity and isotropy; Mathematical basis; Elements of matrix algebra.
2. Stresses: Body and surface forces; Stress tensor; Principal stresses. Stress tensor's invariants; Spherical and deviatoric stresses.
3. Deformation and flow: Material and spatial description; Deformation.
4. Fundamental laws of Continuum Mechanics: Mass conservation; Conservation of linear momentum; Conservation of angular momentum; Conservation of energy. 
5. Constitutive relations: Ideal materials; Classical constitutive relations and equations of state; Elastic solids. 
6. Mathematical models: Linear elastic solids; Initial and boundary conditions; Generic transport equation.
7. Finite volume discretisation: Main concepts and ideas of the Finite Volume method; 3D problems in domains of arbitrary shapes. 
8. Finite element discretisation: Principle of virtual work; Finite element discretisation; Linear elastic finite element model; Assembly of element and global stiffness matrix; Shape functions; Numerical quadrature; Mapping of elements; Solution of the finite element equations.
9. Application to vehicle structural analysis: Performing solid mechanics (linear and nonlinear) analyses;
- Setting up a model: understanding the steps involved in setting up finite element and finite volume models, including choosing the solution domain, material models, initial/boundary conditions, run parameters (e.g. tolerances, time-step size, discretisation schemes), running a model, and post processing the results;
- Understanding and quantifying errors: understanding and distinguishing between the different types of error present in a simulation e.g. discretisation error, linearisation/iteration error, flawed mathematical model;
- Verification and validation of results.

Mini project:
Students will be assigned into groups to work on mini projects on the topics of relevant to the components of the course. They will be assessed through a 8-mins presentation followed by 2 min Q&A session. The findings should also be submitted in the form of a report in which every team member is expected to contribute.

Two homework assignments will be set during the course of the trimester. Students will typically be given two weeks to complete each assignment.

Joint Module Coordinators:
Zhaokai Li, Liming Ma

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Curricular information is subject to change

Learning Outcomes:

On successful completion of this subject the student will be able to:
1. Grasp the basics of continuum mechanics, stress analysis and deformation principles, along with gaining the ability to use the necessary mathematical tools like tensor algebra.
2. Understand fundamental laws of continuum mechanics, including mass, momentum, angular momentum, and energy conservation.
3. Develop skills in material behaviour understanding, constitutive relations, and error identification for accurate vehicle structural analysis.
4. Understand the basics of Finite Volume and Finite Element methods for 3D problems, including matrix assembly, shape functions, and numerical techniques.
5. Apply these methods to analyze vehicle structures, setting up models, defining conditions, managing parameters, and interpreting results, while evaluating errors and ensuring validation.

Student Effort Hours: 
Student Effort Type Hours
Autonomous Student Learning




Small Group




Approaches to Teaching and Learning:
Module delivery is based around weekly lectures, and anticipated to undertake a concluding mini-project as part of the course requirements. A project-based learning approach is taken in lectures and tutorials, whereby the theory is taught through simulations and practical examples. In addition, a comprehensive set of course notes is provided, which allow students to master individual topics at their own pace. The lecturers are very approachable and are always available to meet with students to discuss any topic for which they require further clarification. 
Requirements, Exclusions and Recommendations

Not applicable to this module.

Module Requisites and Incompatibles
MEEN2003W - Solid Mechanics 1, MEEN3002W - Solid Mechanics 2

Additional Information:
This module is delivered overseas and is not available to students based at the UCD Belfield or UCD Blackrock campuses

Assessment Strategy  
Description Timing Open Book Exam Component Scale Must Pass Component % of Final Grade

Not yet recorded.

Carry forward of passed components
Remediation Type Remediation Timing
In-Module Resit Prior to relevant Programme Exam Board
Please see Student Jargon Buster for more information about remediation types and timing. 
Feedback Strategy/Strategies

• Group/class feedback, post-assessment

How will my Feedback be Delivered?

Not yet recorded.

Reading List:
1. Course Notes (provided).
2. Continuum Mechanics:
G. E. Mase, Theory and Problems of Continuum Mechanics, Schaum's Outline Series, McGraw-Hill, Inc. 1970 (selected chapters)
3. Finite Elements:
-The Finite Element Method for Engineers by Kenneth H. Huebner, Donald L. Dewhirst , Ted G. Byrom, Douglas E. Smith
4. Finite Volume:
-The Finite Volume Method in Computational Fluid Dynamics An Advanced Introduction with OpenFOAM® and Matlab by F. Moukalled , L. Mangani , M. Darwish.

Suggested reading:
1. Continuum Mechanics:
-Nonlinear Continuum Mechanics for Finite Element Analysis by Javier Bonet, Richard D. Wood.
2. Finite Elements:
-Practical Finite Element Analysis by Nitin S. Gokhale, Sanjay S. Deshpande, Sanjeev V. Bedekar, Anand N.
3. Finite Volume:
-Computational Methods for Fluid Dynamics, Ferziger and Peric
-An Introduction to Computational Fluid Dynamics by H. K. Versteeg