FEAPpv - - A Finite Element Analysis Program
Personal Version 4.1 User Manual
Robert L. Taylor
Department of Civil and Environmental Engineering
University of California at Berkeley
Berkeley, California 94720-1710
E-Mail: rlt@ce.berkeley.edu
September 2017
Contents
1 Introduction 1
2 Problem Definition 3
2.1 Execution of FEAPpv and Input/Output Files. . . . . . . . . . . . . . 4
2.2 Modification of Default Options . . . . . . . . . . . . . . . . . . . . . . 4
3 Manual Organization 6
4 Input Records 7
4.1 Constants . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8
4.2 Parameters . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8
4.3 Expressions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9
4.4 Functions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10
5 Mesh Input Data 12
5.1 Start of Problem and Control Information . . . . . . . . . . . . . . . . 12
5.2 Global Data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14
5.3 Nodal Coordinate and Element Connections . . . . . . . . . . . . . . . 14
5.3.1 The COORdinate Command . . . . . . . . . . . . . . . . . . . . 15
5.3.2 The ELEMent Command . . . . . . . . . . . . . . . . . . . . . 16
5.3.3 The BLOCk Command . . . . . . . . . . . . . . . . . . . . . . . 17
5.3.4 The BLENd Command . . . . . . . . . . . . . . . . . . . . . . . 20
5.4 Coordinate and Transformation Systems . . . . . . . . . . . . . . . . . 23
5.4.1 Coordinate Transformation . . . . . . . . . . . . . . . . . . . . 25
5.5 Regions and Element Groups . . . . . . . . . . . . . . . . . . . . . . . 26
5.6 Nodal Boundary Condition Inputs . . . . . . . . . . . . . . . . . . . . . 26
5.6.1 Basic input form. . . . . . . . . . . . . . . . . . . . . . . . . . . 27
5.6.2 Edge input form. . . . . . . . . . . . . . . . . . . . . . . . . . . 28
5.6.3 Coordinate input form. . . . . . . . . . . . . . . . . . . . . . . . 29
5.6.4 Hierarchy of input forms. . . . . . . . . . . . . . . . . . . . . . . 29
5.6.5 Time dependent load functions . . . . . . . . . . . . . . . . . . 30
5.7 Surface Loading . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31
5.8 INCLude and LOOPing: Data reuse . . . . . . . . . . . . . . . . . . . 34
i
CONTENTS ii
5.8.1 Include Commands in Mesh Input . . . . . . . . . . . . . . . . . 34
5.8.2 READ and SAVE Commands in Mesh Input . . . . . . . . . . . 34
5.8.3 LOOP-NEXT to replicate mesh parts . . . . . . . . . . . . . . . 35
6 Element Library 40
7 Material Models 47
7.1 Orthotropic Linear Elastic Models . . . . . . . . . . . . . . . . . . . . . 47
7.2 Isotropic Linear Elastic Models . . . . . . . . . . . . . . . . . . . . . . 49
7.3 Isotropic Finite Deformation Elastic Models . . . . . . . . . . . . . . . 50
7.3.1 St. Venant-Kirchhoff . . . . . . . . . . . . . . . . . . . . . . . . 51
7.3.2 Neo-Hookean and Modified Neo-Hookean Models . . . . . . . . 51
7.4 Rayleigh Damping . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 53
7.5 Viscoelastic Models . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 53
7.6 Plasticity Models . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 55
7.7 Heat Conduction Material Models . . . . . . . . . . . . . . . . . . . . . 56
7.8 Mass Matrix Type Specification . . . . . . . . . . . . . . . . . . . . . . 56
7.9 Element Cross Section and Load Specification . . . . . . . . . . . . . . 57
7.9.1 Resultant formulations . . . . . . . . . . . . . . . . . . . . . . . 57
7.10 Miscellaneous Material Set Parameter
Specifications . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 58
8 End and Miscellaneous Commands 60
9 Mesh Manipulation Commands 61
9.1 The TIE Command . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 61
9.2 The LINK Command . . . . . . . . . . . . . . . . . . . . . . . . . . . . 62
10 Command Language Programs 63
10.1 Problem Solving . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 65
10.1.1 Solution of Non-linear Problems . . . . . . . . . . . . . . . . . . 66
10.1.2 Solution of linear equations . . . . . . . . . . . . . . . . . . . . 68
10.2 Transient Solutions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 69
10.2.1 Quasi-static solutions . . . . . . . . . . . . . . . . . . . . . . . . 69
10.2.2 First order transient solutions . . . . . . . . . . . . . . . . . . . 71
10.2.3 Second order transient solutions . . . . . . . . . . . . . . . . . . 72
10.3 Transient Solution of Linear Problems . . . . . . . . . . . . . . . . . . 73
10.4 Time Dependent Loading . . . . . . . . . . . . . . . . . . . . . . . . . . 74
10.5 Continuation Methods: Arclength Solution . . . . . . . . . . . . . . . . 76
10.6 Augmented Solutions . . . . . . . . . . . . . . . . . . . . . . . . . . . . 77
10.7 Time History Plots . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 77
10.8 Viewing Solution Data: SHOW Command . . . . . . . . . . . . . . . . 78
10.9 Re-executing Commands: HISTORY Command . . . . . . . . . . . . . 79
CONTENTS iii
10.10Solutions Using Procedures . . . . . . . . . . . . . . . . . . . . . . . . 79
10.11Output of Element Arrays . . . . . . . . . . . . . . . . . . . . . . . . . 81
11 Plot Outputs 82
11.1 Screen Plots . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 82
11.2 PostScript Plots . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 85
A Mesh Manual 90
B Mesh Manipulation Manual 163
C Solution Command Manual 169
D Plot Manual 230
Chapter 1
INTRODUCTION
During the last several years, the finite element method has evolved from a linear struc-
tural analysis procedure to a general technique for solving non-linear partial differential
equations. An extensive literature exists on the method describing the theory necessary
to formulate solutions to general classes of problems. It is assumed that the reader is
familiar with the finite element method as describe in popular reference books (e.g.,
The Finite Element Method, 7th edition, by O.C. Zienkiewicz, R.L. Taylor and J.Z.
Zhu
[1]
and The Finite Element Method for Solid & Structural Mechanics, 7th edition,
by O.C. Zienkiewicz, R.L. Taylor and D.D. Fox
[2]
) and desires either to solve a specific
problem or to generate new solution capabilities.
The Finite Element Analysis Program - Personal Version (FEAPpv) is a computer
analysis system designed for:
1. Use in an instructional program to illustrate performance of different types of
elements and modeling methods;
2. In a research, and/or applications environment which requires frequent modifi-
cations to address new problem areas or analysis requirements.
The computer system has been developed primarily for Apple, UNIX and Windows
environments and includes an integrated set of modules to perform input of data de-
scribing a finite element model, construction of solution algorithms to address a wide
range of applications, and graphical and numerical output of solution results.
A problem solution is constructed using a command language concept in which the
solution algorithm is written by the user. Accordingly, with this capability, each user
may define a solution strategy which meets specific needs. There are sufficient com-
mands included in the system for applications in structural or fluid mechanics, heat
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