EDACFEM

Short Description

Toolkit for MATLAB-based FEM calculations developed by the Engineering Design and Computing Laboratory (EDAC) at ETH Zurich.

Introduction

This work provides a linear truss and beam FE simulation environment written in MATLAB. The simulation environment supports linear truss elements, Euler-Bernoulli beam elements, and Timoshenko beam elements. It further supports the introduction of global accelerations such as gravity and truss buckling analysis. A variety of input methods are supported, these are specifically tailored towards simplifying the integration of the FE simulation environment in numerical optimization schemes. The code distinguishes itself through its fast simulation speeds even for large beam and truss structures in both 2D and 3D. With this environment, researchers and design practitioners can easily simulate the mechanical response of complex bar structures without the need for interfacing with commercial FE software through cumbersome APIs.

Project Layout

• lib/elements: contains beam and truss element implementations and solvers
• lib/general: contains helper functions for simulation and input
• lib/plot: contains plotting functions
• src/examples: set of examples showing the different input types
• FEM_toolkit_examples.m: file to run the examples provided
• config.m: file to configure the MATLAB path to include the toolbox

Requirements

Matlab 2020b or higher is required.

The additional package requirements for the beam calculations are:

• MATLAB Parallel Computing Toolbox

Installation

To run the toolbox, it only needs to be added to the MATLAB path. A configuration script config.m is provided to automate this step. This config script has three options as shown in FEM_toolkit_examples.m.

• permanent: permanently adds the current toolbox location to the MATLAB path.
• temp: adds the current toolbox location to the MATLAB path until restart.
• pass: do nothing, user must manually add the toolbox to the MATLAB path.

Examples

To run the provided examples, just run the provided MATLAB script FEM_toolkit_examples.m.

Problem User Inputs

Three different methods are currently implemented to supply the input parameters. The import method script_full is shown in example_0 using trusses, the import method script_simplified is shown in example_02 using Timoshenko beams, and the import method pbFC is shown in example_03 using Euler-Bernoulli beams. All three examples can be run from the main directory using the FEM_toolkit_examples.m file.

Group	Name	Size	Unit	Description
Geometry	p	[n x 2] [n x 3]	mm	Nodal coordinates of n nodes in 2D or 3D.
Geometry	b	[m x 2]	-	List of m pairs of node IDs connected by elements.
Load / Boundary	F	[i x 6] {F_1,F_2}	N Nmm mm rad	List of i prescribed loads/moments/displacements/rotations in the form [ID type X Y Z mag]. See additional information in the section below for specifics. Mutliple load cases can be submitted at the same time, to do so add one list per load case to a cell array called F during boundary condition initialization.
Load / Boundary	C	[j x DOF] {C_1,C_2}	-	List of j restricted displacements where DOF is the number of possible displacements and rotations dependent on the element and problem setting. For each DOF, the DOF can be fixed with an entry of 1. Mutliple load cases can be submitted at the same time, to do so add one list per load case to a cell array called C during boundary condition initialization.
Element Properties	E	1 or m	MPa	Elastic modulus for all elements or each individual element.
Element Properties	A	1 or m	mm2	Cross-sectional area for all elements or each individual element.
Element Properties	ρ	1 or m	t/mm3	Density for all elements or each individual element. Only further used if selfweight is active.
Element Properties	ν	1 or m	-	Poisson’s ratio for all elements or each individual element. Only used for beam structures.
Options	elemType	-	-	Provide type ‘truss’ or type ‘beam’
Options	elemSubtype	-	-	Provide type ‘linear’ for truss and type ‘eulerbernoulli’ or ‘timoshenko’ for beams.
Options	selfweight	Boolean	-	Toggle if structure shall be evaluated under selfweight
Options	g	[1 x 1] [1 x 3]	mm/s2	Gravity constant or gravity vector. Per default, the gravity points in negative z direction. Only needed if selfweight is active.
Options	Buckling	Boolean	-	Toggle if buckling evaluation shall be performed. Only supported for truss structures.
Options	Shape	-	-	Cross-sectional shape of the elements. Only ‘circle’ supported. Only needed if buckling is active.

Boundary Conditions and Loads

• Trusses:

  • C (2D): [id X Y]
  • C (3D): [id X Y Z]
  • F (2D): [id type X Y 0 mag]
  • F (3D): [id type X Y Z mag]
  • type: 1: force, [ ], 3: displacement, [ ]

• Beams:

  • C (3D): [id X Y Z Alpha Beta Gamma]
  • F (3D): [id type X Y Z mag]
  • type: 1: force, 2: moment, 3: displacement, 4: rotation

Truss Outputs

Group	Name	Size	Unit	Description
Force	F	[n x 2] [n x 3]	N	Global Nodal Forces
Displacement	u	[n x 2] [n x 3]	mm	Global Nodal Displacements
Force	N	[m x 1]	N	Axial Force
Stress	S	[m x 1]	MPa	Axial Stress
Strain	A	[m x 1]	-	Axial Strain
Length	ρ	[m x 1]	mm	Axial Length Delta

Beam Outputs

Group	Name	Size	Unit	Description
Force Moment	F	[n x 6]	N Nmm	Global Nodal Forces / Moments
Displacement Rotation	u	[n x 6]	mm rad	Global Nodal Displacements / Rotation
Force	N	[m x 1]	N	Axial Force
Force	Qy / Qz	[m x 1]	N	Lateral Forces
Moment	Tt	[m x 1]	Nmm	Torsional Moment
Moment	Mymax Mzmax	[m x 1]	Nmm	Maximum Bending Moments
Stress	Sx / Sy / Sz	[m x 1]	MPa	Axial / Shear Stress
Stress	S1eq / S2eq Teq	[m x 1]	MPa Nmm	Equivalent Stresses / Moment
Stress	Smises	[m x 1]	MPa	Von Mises Stress

Authors

• Dr. Tino Stankovic
• Dr. Tian 'Tim' Chen
• Dr. Thomas S. Lumpe
• Joël N. Chapuis
• Marc Wirth
• Andreas Walker
• Jonas Schwarz