| Subject name (in Hungarian, in English) | Fundamentals of finite element method | |||
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Fundametals of the finite element method
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| Neptun code | BMEGEMMBXVE | |||
| Type | study unit with contact hours | |||
| Course types and number of hours (weekly / semester) | course type: | lecture (theory) | exercise | laboratory excercise |
| number of hours (weekly): | 2 | 0 | 1 | |
| nature (connected / stand-alone): | - | - | coupled | |
| Type of assessments (quality evaluation) | mid-term grade | |||
| ECTS | 3 | |||
| Subject coordinator | name: | Dr. Kossa Attila | ||
| post: | associate professor | |||
| contact: | kossa@mm.bme.hu | |||
| Host organization | Department of Applied Mechanics | |||
| http://www.mm.bme.hu | ||||
| Course homepage | http://www.mm.bme.hu/targyak/?BMEGEMMBXVE | |||
| Course language | hungarian, english | |||
| Primary curriculum type | mandatory | |||
| Direct prerequisites | Strong prerequisite | BMEGEMMBXM4 | ||
| Weak prerequisite | ||||
| Parallel prerequisite | ||||
| Milestone prerequisite | at least obtained 0 ECTS | |||
| Excluding condition | BMEGEMMAGMV, BMEGEMMAGM5 | |||
Aim
The main goal of the subject is to introduce the students to the basics of the finite element method primarily through solving elasticity-related problems. The subject aims to cover the following main topics: computation of deformations in rod structures using matrix formalism; fundamentals of elasticity theory; principle of minimum potential energy; finite element discretization; definition of shape functions; formulation of finite element equations; solution strategies for finite element problems; introduction to plane tension/compression and bending beam elements; finite element analysis of plane tension/compression and bending beam structures; introduction to plane quadrilateral elements; computation of stiffness matrix for plane quadrilateral elements; solution of plane problems using the finite element method; introduction to Gauss quadrature; analytical and finite element analysis of longitudinal vibrations in rods; finite element computation of bending vibrations in beams; introduction of consistent and lumped mass matrices; estimation of natural frequencies.
Learning outcomes
Competences that can be acquired by completing the course
Knowledge
Knows the essence and limitations of the finite element method, as well as the mini-minimum principle of total potential energy and the principle of virtual work; Knows the basic equations of linear elasticity and the structure of the finite element method; Knows the concept of form function and the concept and meaning of discretization; Understands methods for solving finite equations and finite element descriptions of bar and beam elements; Understands the description of three- and four-node elements in a plane; Understands the concept of quadratic element and Gaussian quadrature; Understands the finite possibilities and limitations of vibrational problems; He is aware of the concept and significance of a consistent mass matrix; He is aware of the basic possibilities of solving nonlinear finite element equations; Students have basic user knowledge in a commercial finite element software.
Ability
Capable of determining the displacements of stressed / compressed bar structures loaded in a plane and the stresses arising in the bars using the finite element method, even by manual calculation; Capable of determining the displacements / rotations of planar loaded / compressed and bent beam structures and the stresses occurring in the beams using the finite element method, even by manual calculation; Able to describe displacement functions within an element from node displacements and rotations using form functions; Prepares and builds a finite element model of elasticity problems using planar elements; Determines the natural frequencies of rods in the case of longitudinal vibration by analytical methods; It gives a finite element estimate of the eigenfrequencies in the case of longitudinal vibration of rods and calculates the oscillation images; It gives a finite element estimate of the natural frequencies in the case of bending vibrations of beams and calculates the oscillation images; Apply Gaussian quadrature even for triple integrals; Interprets the results produced by finite calculations; It solves nonlinear equations using the Newton-Raphson method.
Attitude
To the maximum of his abilities, he strives to carry out his studies at the highest possible standard, acquiring in-depth and independent knowledge; Collaborates with the instructor and fellow students in expanding knowledge, strives for independent work; It also expands its knowledge by continuously acquiring knowledge, supplementing the parts of the material described in the lessons; It is also open to the use of information technology and computer tools (word processing computer software, mathematical software, image editing software, etc.); Open to learning about and routinely using the tools needed to solve tasks; It strives for an accurate, error-free and precise task solution.
Independence and responsibility
He feels a responsibility to set an example to his peers by the quality of his work and adherence to ethical standards; He feels a responsibility to apply the knowledge acquired during the course properly, given the limits of its validity; Openly accepts well-founded critical remarks; Accepts the framework of cooperation, depending on the situation, he is able to do his work independently or as part of a team; Checks the reliability of the results obtained using information technology tools.
Teaching methodology
The subject consists of two hours of theoretical classes and one hour of laboratory sessions per week. The understanding of the theoretical content presented during the lectures is aided by the demonstration of sample problems in the laboratory. The derivation of the most important theoretical topics takes place on the board during the lectures to facilitate collaborative work and enhance students' comprehension of the subject matter. Additionally, using a projector, we present supplementary materials. Animated visuals and sample problems projected during the theoretical classes further support the students' learning process. The materials used in both lectures and labs will be available for download to the students. Regular consultations will be provided throughout the semester.
Support materials
Textbook
Editor: Ádám Kovács: Finite element method. ISBN 9789632795393. 2011.
Lecture notes
Online material
Validity of the course description
| Start of validity: | 2023. August 1. |
| End of validity: | 2025. July 15. |
General rules
The students have the opportunity to work on four homework assignments. In the first part of the homework, they are required to solve a given mechanical problem using finite element software, while in the second part, they have the option to solve the finite element problem manually by applying their own program code. The homework assignments must be submitted by the deadline, and late submissions or revisions are not allowed. Submitting the homework assignments is not mandatory. A total of 100 points can be earned with the homework assignments. To verify the usage of the software, the students must complete seven proficiency tests in which they have to repeat a given task using the finite element software. Fulfilling these tests is mandatory, and they can also earn extra points. Additional extra points can be earned during the laboratory sessions by solving test questions.
Assessment methods
Detailed description of mid-term assessments
| Mid-term assessment No. 1 | ||
| Type: | diagnostic assessment | |
| Number: | 7 | |
| Purpose, description: | During the proficiency tests, the students have to repeat a pre-issued and worked-out example in the finite element software a total of 7 times throughout the semester. As a result, students gain practice in using commercial finite element software, and they can apply this knowledge in other subjects in the future. The topics of the examined tasks cover the theoretical content discussed during the semester. The worked-out examples facilitate the understanding of the theoretical material. By completing each proficiency test, students can earn +1 credit point. | |
| Mid-term assessment No. 2 | ||
| Type: | formative assessment, simple | |
| Number: | 4 | |
| Purpose, description: | Partial performance evaluations consist of elaborated homework assignments. A total of four homework assignments are possible, but students can submit any number of them at their discretion. There is no designated mandatory homework assignment. It is essential to note that there is no prescribed minimum score for the homework assignments, but late submissions or revisions are not allowed. The homework assignments have two main parts: solving a given problem using finite element software, and solving the same problem through manual calculations with the help of their own program code. During the process of solving the homework assignments, students have the opportunity to gain practice in using symbolic and numerical mathematical software. | |
Detailed description of assessments performed during the examination period
The subject does not include assessment during the examination period.
The weight of mid-term assessments in signing or in final grading
| ID | Proportion |
|---|---|
| Mid-term assessment No. 1 | 7 % |
| Mid-term assessment No. 2 | 100 % |
The weight of partial exams in grade
There is no exam belongs to the subject.
Determination of the grade
| Grade | ECTS | The grade expressed in percents |
|---|---|---|
| very good (5) | Excellent [A] | above 90 % |
| very good (5) | Very Good [B] | 85 % - 90 % |
| good (4) | Good [C] | 70 % - 85 % |
| satisfactory (3) | Satisfactory [D] | 55 % - 70 % |
| sufficient (2) | Pass [E] | 40 % - 55 % |
| insufficient (1) | Fail [F] | below 40 % |
The lower limit specified for each grade already belongs to that grade.
Attendance and participation requirements
Must be present at at least 70% (rounded down) of lectures.
At least 70% of laboratory practices (rounded down) must be actively attended.
Special rules for improving, retaken and replacement
The special rules for improving, retaken and replacement shall be interpreted and applied in conjunction with the general rules of the CoS (TVSZ).
| Can the submitted and accepted partial performance assessments be resubmitted until the end of the replacement period in order to achieve better results? | ||
| NO | ||
| Taking into account the previous result in case of improvement, retaken-improvement: | ||
| new result overrides previous result | ||
| The way of retaking or improving a partial assessment for the first time: | ||
| partial assesment(s) in this group cannot be improved or repeated, the final result is assessed in accordance with Code of Studied 122. § (6) | ||
| Completion of unfinished laboratory exercises: | ||
| missed laboratory practices may be performed in the repeat period, non-mandatory | ||
| Repetition of laboratory exercises that performed incorrectly (eg.: mistake in documentation) | ||
| incorrectly performed laboratory practice (e.g. Incomplete/incorrect report) can be corrected upon improved re-submission | ||
Study work required to complete the course
| Activity | hours / semester |
|---|---|
| participation in contact classes | 42 |
| preparation for laboratory practices | 14 |
| elaboration of a partial assessment task | 16 |
| additional time required to complete the subject | 18 |
| altogether | 90 |
Validity of subject requirements
| Start of validity: | 2023. August 1. |
| End of validity: | 2025. July 15. |
Primary course
The primary (main) course of the subject in which it is advertised and to which the competencies are related:
Mechanical engineering
Link to the purpose and (special) compensations of the Regulation KKK
This course aims to improve the following competencies defined in the Regulation KKK:
Knowledge
- Student is familiar with the general and specific mathematical, scientific and social principles, rules, contexts and procedures needed to operate in the field of engineering.
Ability
- Student has the ability to apply the general and specific mathematical, scientific and social principles, rules, relationships and procedures acquired in solving problems in the field of engineering.
Attitude
- Student is open and receptive to learning, embracing and authentically communicating professional, technological development and innovation in engineering.
Independence and responsibility
- Student has the ability to work independently on engineering tasks.
Prerequisites for completing the course
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Knowledge type competencies
(a set of prior knowledge, the existence of which is not obligatory, but greatly facilitates the successful completion of the subject) |
none |
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Ability type competencies
(a set of prior abilities and skills, the existence of which is not obligatory, but greatly contributes to the successful completion of the subject) |
none |