Mechanical APDL Structural Analysis Guide

15.4. Using Nonlinear General Beam Sections

The nonlinear general beam section (SECTYPE,,GENB) is an abstract cross section type that allows you
to define axial, flexural, torsional, and transverse shear behavior as a function of axial strain, bending
curvature, twist, and transverse shear strains.

The generalized section form of input does not require cross section geometry data or material data
independently. For evaluating mass matrices, the program assumes a unit area of cross section. This
form of data is useful for including an experimentally measured nonlinear response of a beam-like
structural component, or for including complex behavior such as cross section distortion (not possible
when using normal beam sections).

Nonlinear general beam sections also allow a nonlinear relationship of transverse shear forces to the
corresponding transverse shear strains. Often, the input of generalized beam sections may be a result
of a prior detailed slice analysis (for example, a segment of pipe analyzed using generalized plane strain
elements).

The behavior of beam elements is governed by the generalized-stress/generalized-strain relationship
of the form:

N

M

M

S

S

A T

T

T

J

1

2

1

2

E

1 E

2

τ

ε

κ

κ





       





       

=

( , )

( , )

( , )

1

2

0

1 G

T

T

( , )

( , )

χ

γ

ε

κ

κ

χ

(^01)
1
2


          


          
γγ
γ
1
2


       


       
I
IE
G
A
A 2 G( , )γ 2 T
where:
N = Axial force
M 1 = Bending moment in plane XZ
M 2 = Bending moment in plane XY
τ = Torque
S 1 = Transverse shear force in plane XZ
S 2 = Transverse shear force in plane XY
ε = Axial strain
κ 1 = Curvature in plane XZ
κ 2 = Curvature in plane XY
χ = Twist of the cross section
γ 1 = Transverse shear strain in plane XZ
γ 2 = Transverse shear strain in plane XY
AE(ε,T) = Axial stiffness as a function of axial strain and temperature
I 1 E(κ 1 ,T) = Flexural rigidity as a function of curvature and temperature in plane XZ
I 2 E(κ 2 ,T) = Flexural rigidity as a function of curvature and temperature in plane XY
JG(χ,T) = Torsional rigidity, as a function of torsion and temperature
A 1 G(γ 1 ,T) = Transverse shear stiffness as a function of shear strain and temperature in plane XZ
Release 15.0 - © SAS IP, Inc. All rights reserved. - Contains proprietary and confidential information
Using Nonlinear General Beam Sections