FEAP - A Finite Element Analysis Program

## FEAP -- Version 8.4

The distribution of FEAP version 8.4 is now available. Several enhancements have been incorporated in the new version. In part these include:

- Hill-Mandel homogenization of representative volume element (RVE) in serial version. Can homogenize thermal properties of material moduli and stresses.
- Multi-scale implementation of Hill-Mandel homogenization of RVE. Can perform analysis using FE^2 method in which RVE receive input of strain, deformation gradient or temperature gradient. Implemented for small and finite strain elastic and inelastic models.
- Anisotropic plasticity using Hill 1948 model. Implemented for small and finite deformations. Yield specified by linear and saturation hardening as well as Swift power law model.
- Load groups generalized to work for multiple instances.
- Generalized concentrated nodal stiffness, damping and mass to work in both serial and parallel versions.
- Added implicit-explicit dynamics option. Permits mixture of elements integrated by explicit or implicit Newmark method.
- Added projection and plot of contours for element history variables.
- Added 'tria'd specification for 3-d sloping boundary specification.
- Added option to display basic form of solution commands during interactive solutions: e.g. help tang -- displays basic form of tang command.
- Added option for 'jpeg' graphics output files.
- Added projection and plot of strain contours.
- Most finite deformation material models coded to use displacement gradient instead of deformation gradient to permit accurate solutions at very small strains.
- Added St.Venant torsion to built in elements.
- Updated to parallel FEAP to work with PETSc 3.4.
- Changed partition options in parallel FEAP, see parallel FEAP manual.
- Added parallel contact.
- Several bug fixes.

SUMMARY NEW COMMANDS:

Mesh Input

- EXPL - sets explicit-implicit element groups
- TRIAd - sets triad for 3-d boundary condition orientation
- PERIodic - generalized to specify thermal and mechanical values for Hill-Mandel

Solution Commands

- HILL - Hill-Mandel homogenization
- Extend user solution commands from 10 to 20.

Plot Commands

- JPEG - jpeg output file option
- HISTory - Contour history variable
- STRAin - Contour strain values.

FEAP is a general purpose finite element analysis program which is designed for research and educational use. Source code of the full program is available for compilation using Windows (Intel compiler), LINUX or UNIX operating systems, and Mac OS X based Apple systems (GNU and Intel compilers).

- Contact

- for further information and distribution costs.

The FEAP program includes options for defining one, two, and three dimensional meshes, defining a wide range of linear and nonlinear solution algorithms, graphics options for displaying meshes and contouring solution values, an element library for linear and nonlinear solids, thermal elements, two and three dimensional frame (rod/beam) elements, plate and shell elements, and multiple rigid body options with joint interactions. Constitutive models include linear and finite elasticity, viscoelasticity with damage, and elasto-plasticity.

The system may also be used in conjunction with mesh generation programs that have an option to output nodal coordinates and element connection arrays. In this case it may be necessary to write user functions to input the data generated from the mesh generation program.

Any problems related to difficulties in achieving a standard installation of the program should be addressed to: feap@berkeley.edu.

## FEAPpv

A small version of the system, called FEAPpv, is available free of any charge. See www.ce.berkeley.edu/feap/feappv for additional information. This program is the companion to the books: "The Finite Element Method, 6th edition, Volumes 1 and 2 (but not Vol 3)", authored by O.C. Zienkiewicz and R.L. Taylor and published by Elsevier, Oxford, 2005.

## MANUALS FOR FEAP Ver 8.4

PDF files for current FEAP manuals may be obtained by downloading the following:

- FEAP Installation Manual: v8.4 - - - (July 2013)
- FEAP User Manual: v8.4 - - - - - - -(December 2013)
- FEAP Example Manual: v8.4 - - - - (July 2013)
- FEAP Input/Output files (zip) - - - - (July 2013)
- FEAP Programmer Manual: v8.4 - - (May 2014)
- FEAP Contact Manual: v8.4 - - - - -(July 2013)
- FEAP Parallel Manual: v8.4 - - - - - (July 2013)
- FEAP FE^2 Manual: v8.4 - - - - - (July 2013)
- FEAP Theory Manual: v8.4 - - - - -(July 2013)

N.B. PDF files require Acrobat Reader to print.

## User Forum

A new user forum for FEAP users has been created at http://feap.berkeley.edu. This is a site to post questions, get answers, and interact with other users. We encourage users to help other users.

## INPUT/OUTPUT FILES FOR FEAP Ver 8.4 TEST PROBLEMS

The file below contains a few simple test problems and the output they produce using FEAP ver 8.4. The file is in 'zip' form.

- Test problems for FEAP v8.4 (zip file) - - - -(July 2013)

## ADDITIONAL ELEMENTS FOR FEAP Ver 7.3 to 8.4

User elements may be added to the FEAP system to extend solution capabilities (See FEAP Programmer Manual). The elements given below are examples of elements which are useful in educational applications to demonstrate the behavior of finite element solutions of classical applications

- Rectangular thin plate element (elmt05.f: Bogner-Fox-Schmit rectangle)
- Rectangular thin plate element (elmt06.f: DKQ rectangle)
- Triangular thin plate element (elmt07.f: DKT triangle)
- Elastic St. Venant torsion element (elmt11.f: Warping and stress function solutions)
- Plastic St. Venant torsion element (elmt12.f: Warping function solution with Mises plasticity and isotropic hardening)

## MATLAB INTERFACE (for older versions of FEAP)

The MATLAB interface is a standard part of versions 8.1 and later.

The MATLAB program permits easy solutions using many different algorithms. An interface for FEAP is provided by the user solution command routine 'umacr3.f' below. This routine permits the output to files of the non-zero values contained in the residual, tangent, mass, or damping matrices. The routine is fully operational with the 7.5 release of FEAP and except for the unsymmetric mass and damping options with release 7.4. The use is quite simple. In the solution command sequence:

- TANG,,-1 ! Form unfactored tangent

- OUTPut TANG ! Output to file 'tang' nonzero terms in tangent.

A simple MATLAB program to use the tangent is

- load tang

- A = spconvert(tang)

Download file from:

A direct link with MATLAB is also available. This permits FEAP to be run from MATLAB and allows for solution options available in MATLAB to be used in the analysis process. The interface is available from David Bindel at the web site listed below.

## LINEAR EQUATION SOLVER INTERFACES

### SGI Solver

The SGI Origin machines have multiprocessor capability and solution of finite element problems using FEAP can be made much more efficient using special solution packages. The routine given below provides an interface to the SGI parallel sparse solver (users must already have the solution package from SGI for this interface to function).

### SuperLU Solver

An interface is available for the general sparse solver SuperLU. General information at: (http://www.cs.berkeley.edu/~demmel/SuperLU.html) Source program at (http://crd.lbl.gov/~xiaoye)

Download the source and create an archive containing the SuperLU routines for double precision real computations and, if necessary, the BLAS routines. (N.B. The SuperLU solver has been tested only in a Linux environment).

Next, download the following feap interface routines (zipped). Compile and link with the main FEAP archive and those for SuperLU created as described above. Use solution command 'splu' to activate the SuperLU solver. Subsequent commands 'tang' or 'utan' will then use SuperLU.

### UMFPACK Solver

An interface is available for the general sparse solver UMFPACK. General information and source may be obtained from: (http://www.cise.ufl.edu/research/sparse/umfpack)

Down load the source and create an archive containing the UMFPACK archive. The interface may be obtained from:

### WSMP Solvers

An interface is available for the sparse solver system WSMP (Watson Sparse Matrix Package, IBM Research). General information and licensing requirements may be obtained from: (http://www.research.ibm.com/math/OpResearch/wsmp.html)

After receiving the source and license, create an archive containing the WSMP program. The FEAP interface may be obtained from:

## Other FEAP Web Sites:

- Sanjay Govindjee Contains examples for user functions as well as a C interface for developing elements, etc.
- David Bindel A MATLAB interface to FEAP which permits simultaneous access to both programs.
- Sandra Klinge A Multiscale program MSFEAP built on FEAPpv.

Last Updated 01 July 2013

*Structural Engineering, Mechanics and MaterialsDepartment of Civil and Environmental EngineeringUniversity of California, Berkeley*

**FEAP - A Finite Element Analysis Program**