| | Module consists of the study units |
Module 4, Design and Mechanics, consists of several module parts, every part has its own learning objectives. The Module overview is given below:
| Course name |
Code |
| 1. Lineare Algebra |
202001210 |
| 2. Mechanics of Materials & Mod. and Prog. 4 |
202000122 |
| 3. Machine Elements |
202000123 |
| 4. Proj. Design Construction & Ac. Skills 4 |
202000124 |
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Aims
Linear Algebra
Work with systems of linear equations, vectors, matrices, subspaces of Rn and explain the connections between these concepts
- determine an echelon form and the reduced echelon form of a matrix
- write a linear system in the form Ax = b
- determine if a linear system is (in)consistent
- determine the solution set of a linear system
- perform operations with vectors and matrices (addition, scalar multiplication, multiplication, transpose, linear combinations
- apply properties of operations with vectors and matrices
- define the concept of inverse of a matrix
- apply properties of an invertible matrix
- calculate the inverse of a regular matrix
- characterize an invertible matrix in terms of its echelon form, its columns (rows), linear systems
- interrelate the solution sets of Ax = b and Ax = 0
- examine the linear (in)dependency of a set of vectors
- explain the concepts of subspace and basis
- determine (a basis for) a subspace (e.g. column space, null space of a matrix)
- compute coordinate vectors w.r.t. a basis
- determine the dimension of a subspace
Work with determinants, eigenvalues, eigenvectors, linear transformations and connect them with the previous concepts
- explain the concept of determinant of a matrix
- compute the determinant of a matrix using cofactor expansion
- apply properties of determinants (w.r.t. row- and column operations and multiplication)
- characterize an invertible matrix in terms of its determinant
- calculate the area of a parallelogram or volume of a parallelepiped using determinants
- explain the concepts of eigenvalue and eigenvector of a matrix
- compute the eigenvalues and eigenvectors of a matrix, using the characteristic equation
- determine if a matrix is diagonalizable
- write a diagonalizable matrix as A = PDP−1
- explain the concept of linear transformation (domain, codomain, images)
- calculate the standard matrix of a linear transformation
- examine properties of linear transformations (one-to-one, onto)
Mechanics of Materials
After the course the student will be able to:
- apply the method of sections to calculate internal loadings, stresses, strains & deformations in slender members:
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- subjected to axial loadings (bars)
- with circular cross section subjected to torsional loadings (shafts).
- with symmetric cross section subjected to transversal loadings, c.q. bending and shear (beams).
- derive the critical load & buckled shape of beams (using Euler buckling theory).
- analyze statically determinate & indeterminate structures.
- determine the second moment of area for composite cross sections.
- understand basic mechanical concepts of a structure, analyze it using correct theoretical models and evaluate the results of a calculation.
Modeling and Programming
As a result of the course a student is able to:
- solve beam equations using MATLAB.
- determine the maximum stresses in a beam using MATLAB.
- write a finite element program to calculate the stresses in a frame with beams.
- optimize the frame geometry using the finite element code and standard optimization routines.
Machine Elements
After the course the student is able to...
- Analyze mechanical design problems using engineering design principles, present alternative solution concepts and make an informed decision
- Mention and characterize machine elements in mechanical design, and analyze them in relation to system specifications
- Evaluate the relation between function, material, connection method, shape, size and cost of machine elements
- Explain design principles for mechanical power transmission systems, including mechanical drives, gears, shafts and bearings, and apply these in a practical context
- Analyze mechanical loads on constructions, machine elements and standardized connection types
- Evaluate simple mechanical constructions and make a justified selection and design using standardized machine elements
Project “Designing a Mechanical Structure”
Within the project, students
- Design a mechanical structure, recognize and implement different phases within such a process: problem formulation; analyzing and establishing design requirements; introducing concept designs; choosing a concept; detailing the design of choice; assigning materials.
- Evaluate different concept designs, choose a concept and justify their choice.
- Apply their earlier knowledge on material science and production techniques from previous modules in the current design project.
- Apply the knowledge gained from “Mechanics of Materials” and “Modeling and Programming” courses on detail design of the chosen concept.
- Utilize stress and strain transformations (using e.g. Mohr’s circle) to calculate principal stresses and strains and apply it in the project.
Academic Skills
- Write a (design-) report for the client.
- Being able to reflect on your own work as a mechanical engineering student and future professional.
Content
This quartile consists of a project assignment and five courses:
Project “Designing a Mechanical Structure”
The aim of the project is to design a functional structure which allows students to integrate their various mechanical design skills. The theoretical knowledge gained by the students during the current module and earlier courses such as Mechanics of materials, Material science, Statics and Machine elements are applied in the project. The project includes designing mechanical components, proper choice of materials and suitable production methods. The assignment is done within groups of 8 students. The subject of the project varies each year, however in principal the project characteristics (structure composed of a number of moving parts) remain the same. The structure is usually made of slender elements (pipes and profiles) with a functional purpose. The project is limited to the conceptual phase and mainly focuses on realizing feasibility and the development of the concept product.
Linear Algebra
In this course of Linear Algebra we mainly focus on systems of linear equations (linear systems). Many real life situations can be modeled as a linear system. Examples are networks (traffic networks, data networks, electrical networks, etc.), economic models, chemical reactions, cryptography (coding of messages), scheduling, computer graphics, GPS.
Linear Algebra starts with an introduction of linear systems which will be described using a (coefficient-) matrix. Already in the first week we learn how to solve linear systems systematically, using a row reduction technique on the coefficient matrix. In the second week we focus on operations vectors and matrices, such as addition, multiplication, inverse and transpose. These operations are a fundamental issue in Linear Algebra. In the third week we deal with sets of vectors with very nice properties: subspaces. It turns out than the properties of subspaces can tell us a lot about the structure of solution sets of linear systems. Here the concepts of linear combination, linear independence, basis and dimension play an important role. In the fourth week we introduce the concept of determinant of a square matrix. We explore its properties and show some interesting interpretations. The fifth week will be about eigenvectors and eigenvalues of a square matrix. These concepts play a crucial role in discrete dynamic systems, which arise in many scientific fields. Finally, in the last week, we examine linear transformations and their properties. Some well-known applications in geometry will be treated as well. Much emphasis is laid on the relations among the various concepts. A case-study will be implemented in each program, to become acquainted with applications of Linear Algebra.
Mechanics of Materials
This course covers how the stiffness and strength of a structure consisting of different members such as bars, beams and shafts can be determined. Stiffness describes the relationship between loads and deflections of a structure and strength refers to stresses and strains occurring in the material.
Modeling and Programming
The Finite Element Method is a key engineering tool for the design of mechanical systems. It can be used to determine internal stresses and deformation of structures due to external loads. A basic form of the Finite Element Method for beam structures will be developed throughout a series of ModPro 4 sessions. The complexity of the systems will gradually increase during the sessions, from 1D truss systems, to single beam calculations, to full truss and beam structures. Optimization methods discussed in ModPro 3 will be used to optimize structure designs.
Machine Elements
This course offers an introduction into mechanical engineering design, in which basic mechanical engineering functions and concepts are discussed systematically. Engineering concepts and design principles are provided to select and design machine elements that are commonly found in mechanical systems and constructions. The relation between function, material, connection method, shape, size and cost of machine elements is discussed in relation to systems specifications. Practical design principles for combining stresses and different types of loading are analyzed. The design of a complete mechanical power transmission system is covered including belt and chain drives, gears, shafts, keys, couplings, seals and bearings. The design of standardized machine elements for connections are discussed including fasteners, springs, machine frames, bolted connections and welded joints.
Academic Skills
In this final module of the year, various aspects of academic skills are addressed; communication in writing, oral presentation and being able to reflect on your own work.
The results of the project have to be presented in a written (design-) report for the client and an oral presentation for a committee.
In an individual assignment the student has to reflect on his own work in the last year and look forward to the future as a student (and professional) in mechanical engineering
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| Bachelor Mechanical Engineering |
| | Required materialsCourse material| See listing at associated study unit(s) |
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Recommended materialsCourse material| See listing at associated study unit(s) |
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