Solid Mechanics

Faculty of Engineering, LTH

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Strukturoptimering FHLN01

Credits: 7.5 . Responsible teacher: Mathias Wallin. Prerequisites: Applied Mathematics or Linear Analysis and Finite Element Method. Teaching: Lectures 28 h, problem sessions 28h, project work 100 h. Individual study: 40 h. Assessment: Written examination and compulsory assignments which are graded. Study period: VT1




To qualify for a final grade it is required that the project assignment is approved as well as passing the mid-term exam. A preliminary course programme for 2020 can be downloaded here

Aims of the course

In stuctural optimization the problem of finding the 'optimal' design is considered. The term 'optimal' design can apply to various aspects and the common features are minimum weight or maximum stiffness of a structure. The course is aimed to give the student knowledge and fundamental understanding of modern tools that are commercially available.

Computer lab

The computer lab can be downloaded here.

A simple example illustrating the Matlab function fzero.m can be downloaded here: main.m, xstar.m and dphidlambda.m

Plot routines for the undeformed and deformed bar structure are found here and here. The extra input arguments are the Areas of the bars and a scale factor.


The project for 2020 is now available here.

Mesh files: LbracketCoarse.mat and LbracketFine.mat.

MMA solver for task c): mma_solver.p. (Updated 27/2-2020)


The project for 2019 is now available here.

NOTE: There is a typo on the last page of the project description above. The size of "dfdx" should be 2 x nelm, and NOT nelm x 2.

Mesh generation: genMesh.m

Design update solver for the design of compliant mechanisms: mma_solver.p

Some additional guidelines and answers to frequently asked questions can be found here.


The project for 2018 is now available here.

Hint:  The syntax for fminbnd is for example

lam=fminbnd(@(lambda) NegDualPhi(lambda,parameter1,parameter2 ....),lam_min,lam_max,OPT);

'OPT' represents a variables that might be supplied to the fimnbnd function, for example OPT=optimset('TolX',1e-12);

Coarse and fine geometry for the topology optimization are given by MBBCoarseMesh.mat and MBBFineMesh.mat.

Routine computing mass matrix for the filtered field, flw2i4m.m.

Routine computing stiffness matrix in displacement boundary value problem with filtered density field, plani4e_rho.m

Routine computing the sensitivity of the compliance with respect to rho_tilde, getdgdrhotilde_el.m

Routine computing the element mass matrix Me0: planei4_m.m.

Routine solving a generalized eigenvalue problem: eigenSM.m.

Old exams


The mid-term exam from 130225 can be downloaded here. Solutions

The mid-term exam from 150224 can be downloaded here. Solutions

The mid-term exam from 180221 can be downloaded here. Solutions

The mid-term exam from 190220 can be downloaded here. Solutions


An introduction to structural optimization,Christensen, P and Klarbring, A
Springer-Verlag, 2008, ISBN: 978-1-4020-8665-6
CALFEM - A finite element toolbox to MATLAB. Studentlitteratur.

Maple files

A maple file containing example 2.5 is available here.

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