# Boundary Elements

## Course Description:

Learning the method of boundary elements to solve engineer problems.

• Semester 9
• Teaching hours 4
• Instructors M. Nerantzaki (Coordinator)

### Prerequisite Knowledge

Students is recommended to have basic knowledge Differential Equations, Mechanics of the rigid body, Mechanics οf Deformable Solids, Computer-based Solution Methods

### Course Units

# Title Description Hours
1 Introduction Introduction. Boundary Elements and Finite Elements. Historical development of the BEM. 1Χ4=4
2 The direct BEM for the Laplace and the Poisson equation Preliminary Mathematical Concepts. The BEM for potential problems in two dimension. 3Χ4=12
3 Numerical Implementation of the ΒΕΜ The BEM with constant boundary elements. Programming the method using Fortran or/and Μatlab. 2Χ4=8
4 Dual Reciprocity The Dual Reciprocity Method. Domains with multiple boundaries. The method of subdomains. 2Χ4=8
5 Applications Torsion of non-circular bars. Deflection of elastic membranes and simply supported plates. Heat transfer problems and Fluid flow problems. 3Χ4=12
6 The ΒΕΜ for nonhomogeneous bodies Solutions of problems with unknown fundamental solutions. Applications. Potential problems to bodies with variable properties. 2Χ4=8

### Learning Objectives

After successful completion of the course, students will be able to: 1. understand the Boundary Element Method and its PC programming, 2. calculate real implementation cases using the relevant software codes.

### Teaching Methods

 Teaching methods Lectures in class. Solve examples and problems in the classroom. Presentations in the Table. Slides PowerPoint. Calculations on PC with software codes. An exemplary application to plates problems with boundary elements and finite element method. Students solve the issues with the help of teachers using FORTRAN και MATLAB on PC. Yes Students are examined in solving engineering problems.

### Student Assessment

• Final written exam: 30%
• Assignments (projects, reports): 70%

### Textbooks - Bibliography

1. Ι. Θ. Κατσικαδέλης, 2012, Συνοριακά Στοιχεία. Θεωρία και Εφαρμογές, Συμμετρία, Αθήνα.
2. J. T. Katsikadelis, 2016, The Boundary Element Method for Engineers and Scientists, 2nd Edition, Elsevier.
3. J. T. Katsikadelis, 2014, The Boundary Element Method for Plate Analysis, 1st Edition, Elsevier.
4. C. A. Brebbia, 1978, The Boundary Element Method for Engineers, Pentech Press, London.
5. P. K. Banerjee, and R. Butterfield, 1981, Boundary Element Methods in Engineering Science, McCraw-Hill, New York.

© 2017 School of Civil Engineering, ΕΜΠ