Mechanical APDL Structural Analysis Guide

with independent material and section definitions, preintegration requires fewer system resources because
numerical integration through the thickness of the shell is not required.

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

T

I

T

T













=





























−

















=

ε

κ

γ

where:

{N} = {N 11 ,N 22 ,N 12 } are membrane stress resultants per unit length

{M} ={M 11 ,M 22 ,M 12 } are bending stress resultants per unit length

{ε} = {ε 11 , ε 22 , ε 12 } are membrane strains

{κ} = {κ 11 ,κ 22 ,κ 12 } are curvatures

{S} = {S 1 ,S 2 } are transverse shear forces per unit length

{γ}={γ 1 ,γ 2 } are transverse shear strains

[A], [B], [D], and [E] are the section-stiffness matrices for membrane, coupling, bending, and shear

behavior, respectively

{MT} are stress resultants caused by a unit rise in temperature on a fully constrained model

{BT} are bending-related stress resultants caused by a unit rise in temperature on a fully constrained

model

TI is the stress-free initial temperature

T is the current temperature

(Subscripts 1 and 2 denote shell surface coordinates as employed by the shell element.)

The preintegrated form of input allows you to import homogeneous section-stiffness constants evaluated
in other analyses or by third-party, special-purpose software tools. For example, defining preintegrated
section stiffnesses [A], [B], and [D] is common in analyses of layered composites, corrugated shells, or
other complex section construction.

16.3.1. Defining a Preintegrated Shell Section

Each of the following commands specifies a particular component quantity necessary for defining a
preintegrated shell section:

Table 16.2: Commands for Specifying Preintegrated Shell Section Data

Command Quantity Defined and Data Specified

Membrane stiffness -- Symmetric part of sub-

matrix [A]

SSPA

A 11 ,A 21 ,A 31 ,A 22 ,A 32 ,A 33 ,T

Coupling stiffness -- Symmetric part of submat-

rix [B]

SSPB [ 1 ]

B 11 ,B 21 ,B 31 ,B 22 ,B 32 ,B 33 ,T

Bending stiffness -- Symmetric part of submat-

rix [D]

SSPD [ 1 ]

D 11 ,D 21 ,D 31 ,D 22 ,D 32 ,D 33 ,T

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Shell Analysis and Cross Sections