Subject Datasheet
Completion requirements
Subject Datasheet
Download PDFI. Subject Specification
1. Basic Data
1.1 Title
FEM for Civil Engineers
1.2 Code
BMEEOTMMSFST01-00
1.3 Type
Module with associated contact hours
1.4 Contact hours
| Type | Hours/week / (days) |
| Lecture | 2 |
| Seminar | 1 |
1.5 Evaluation
Exam
1.6 Credits
4
1.7 Coordinator
| name | Dr. Ádány Sándor |
| academic rank | Professor |
| adany.sandor@emk.bme.hu |
1.8 Department
Department of Structural Mechanics
1.9 Website
1.10 Language of instruction
hungarian
1.11 Curriculum requirements
Compulsory in the Structural Engineering (MSc) programme
1.12 Prerequisites
1.13 Effective date
1 September 2025
2. Objectives and learning outcomes
2.1 Objectives
The goal of the subject is to present the theoretical bases of the finite element method and its practical application to typical structural engineering problems. The classic approach to the finite element method will be followed in presenting the basic idea of the method, the element types, the applied interpolation functions, the various matrices and the basic steps of their construction, the resulting system of equation and the solution techniques of it. All these will be demonstrated and practiced through examples, showing how the various structure types (trusses, beams, frames, plates, shells, 3D solids) can be analysed. An introduction to nonlinearities from various sources will be given, with special focus on the effect and handling of geometric nonlinearity. By completing the subject, this knowledge will enable the student to accomplish tasks related to civil engineering problems.
2.2 Learning outcomes
Upon successful completion of this subject, the student:
A. Knowledge
1. knows the differential equations of basic engineering structures,
2. familiar with the vectors and matrices used in the FEM,
3. knows the calculation methods of the typical shape functions of 1-, 2- and 3-dimensional elements.
4. familiar with the specific characteristics of the finite element models of trusses, beams, plates, shells and solid elements,
5. familiar with the physical meaning of certain elements of the stiffness matrix,
6. familiar with the formulation of boundary value problem in a mechanical problem,
7. knows the variational formulation of mechanical problems,
8. understands the methodology on how the geometric nonlinearity is taken into account,
B. Skills
1. produces the base function of an element according to the required continuity condition,
2. selects the required steps for the calculation of an arbitrary entry of he stiffness matrix of a finite element,
3. constructs the boundary conditions according to behaviour of the mechanical model,
4. during a numerical analysis chooses appropriate element with respect to the mechanical problem,
5. during a numerical analysis chooses the relevant parameters for the mechanical problem,
C. Attitudes
1. works together with the tutor/lecturer and the fellow students while learning,
2. endeavors to discover and routinely use the tools necessary to the problem solving of structural mechanical problems,
3. endeavors to the precise and error-free problem solving,
4. aspires to prepare a well-organized documentation in writings, and pursues the precise self-expression in oral communication,
D. Autonomy and Responsibility
1. independently carries out the conceptual and numerical analysis of structural engineering problems, based on the literature,
2. is open to accept well-founded critical comments.
2.3 Methods
Lectures, exercises, oral and written communication, application of IT tools and technologies, individual assignment.
2.4 Course outline
1. Displacement method, differential equation of basic mechanical problems
2. Solution of a 2D-frame problem with matrix displacement method, stiffness matrix
3. Generalization of the matrix displacement method
4. Tools of the FEM
5. 1D elements, base functions, matrices of elements
6. FEM formulation of 2D plane elements
7. FEM formulation of a Kirchhoff-plate model
8. FEM formulation of a Mindlin-plate model
9. Application of shell elements in FEM
10. FEM formulation of 3D elements
11. Formulation of mechanical problems, strong and weak solutions
12. Consideration of geometric nonlinearities, second order theories
13. Special questions of finite element techniques
14. Summary
The above programme is tentative and subject to changes due to calendar variations and other reasons specific to the actual semester. Consult the effective detailed course schedule of the course on the subject website.
The above programme is tentative and subject to changes due to calendar variations and other reasons specific to the actual semester. Consult the effective detailed course schedule of the course on the subject website.
2.5 Study materials
Zienkiewicz, O.C. . Taylor, R. L.: The finite element method I-III,
Bojtár - Gáspár: Végeselemmódszer építőmérnököknek
2.6 Other information
Attendance at lectures is mandatory.
Students attending tests/exams must not communicate with others without explicit permission during the test/exam, and must not have an electronic or non-electronic device capable of communication switched on.
A signature obtained previously will remain valid at a re-registering for the subject, but the new results are to be considered nevertheless.
2.7 Consultation
The instructors are available for consultation during their office hours, as advertised on the department website. Special appointments can be requested via e-mail.
This Subject Datasheet is valid for:
2025/2026 semester II
II. Subject requirements
Assessment and evaluation of the learning outcomes
3.1 General rules
Evaluation of learning outcomes described in Section 2.2. is based on two mid-term written checks, and an oral exam.
The duration of each mid-term test is 90 minutes.
Mid-term tests below 40% are regarded unsuccessful.
The dates of checks can be found in the "Detailed semester schedule" on the website of the subject.
3.2 Assessment methods
| Assessment Name (Type) | Code | Assessed Learning Outcomes |
|---|---|---|
| Mid-term written check 1 | MT1 | A.1-A.4; B.1-B.2 |
| Mid-term written check 2 | MT2 | A.1-A.8; B.3-B.4 |
| Exam (oral) | E | A.1-A.8; B.1-B.5; C.2-C.4; D.1-D.2 |
The dates of deadlines of assignments/homework can be found in the detailed course schedule on the subject’s website.
3.3 Evaluation system
| Code | Weight |
|---|---|
| MT1 | 25% |
| MT2 | 25% |
| E | 50% |
| Total | 100% |
3.4 Requirements and validity of signature
A student is to obtain signature and have eligibility for the exam if all of the followings requirements met:
-participated in 70% of the contact hours,
-all mid-term tests are successful (after retakes if any),
-the average of the tests reaches or exceeds 50%.
-the weighted average of the mid-terms reaches or exceeds 50%.
3.5 Grading system
| Grade | Score (P) |
|---|---|
| excellent (5) | 85≤P |
| good (4) | 75≤P<85% |
| satisfactory (3) | 65≤P<75% |
| pass (2) | 50≤P<65% |
| fail (1) | P<50% |
3.6 Retake and repeat
The mid-term test with lower result can be retaken in a summarizing retake test.
We use the better result from the original and the retake to calculate the R average.
There is no second retake option.
3.7 Estimated workload
| Activity | Hours/Semester |
|---|---|
| contact lesson | 14×3=42 |
| preparation for lessons during the semester | 14×1,5=21 |
| preparation for the checks | 2×12=24 |
| preparation of homeworks | 7 |
| preparation for the oral exam | 26 |
3.8 Effective date
1 September 2025
This Subject Datasheet is valid for:
2025/2026 semester II