Comput Visual Sci
DOI 10.1007/s00791-010-0147-z
REGULAR ARTICLE
Realization of an integrated structural design process:
analysis-suitable geometric modelling and isogeometric analysis
R. Schmidt · J. Kiendl · K.-U. Bletzinger ·
R. Wüchner
Received: 1 March 2010 / Accepted: 1 October 2010
© Springer-Verlag 2011
Abstract Increasing complexity in structural shapes, the
need for more detailed and precise numerical simulations,
and shorter product development times request a tightly con-
nected interaction within the design software environment
since both fields, geometric design and structural analy-
sis, rely on the results of each other. Therefore, this paper
proposes an integrated design process, which is predicated
on a NURBS-based CAD environment as well as on the
NURBS-based isogeometric analysis, and substantiates in a
mechanical point of view. The presented investigations are
concentrated on thin-walled structures. In this paper several
issues, e.g. continuity conditions associated with the applied
finite element type, arising from the increased challenges
for the geometric modelling within an integrated design pro-
cess are identified and solution strategies are discussed. Fur-
thermore, general analysis-aware modelling guidelines are
derived. The paper concludes by exemplifying the com-
plete integrated structural design process for a structural
part.
Keywords Integrated structural design process ·
Integration of CAD and CAE · Isogeometric analysis ·
NURBS · Analysis-suitable geometric modelling
1 Introduction
The incompatibility of state of the art technologies for geo-
metric modelling and mechanical simulation and their inten-
Communicated by Hans-Joachim Bungartz.
R. Schmidt (
B
) · J. Kiendl · K.-U. Bletzinger · R. Wüchner
Lehrstuhl für Statik, Technische Universität München, Arcisstr. 21,
80333 Munich, Germany
e-mail: R.Schmidt@bv.tum.de
sive use inside the product development process requires the
development of an integrated framework. In the past, two
possible methodologies have been presented to approach an
integrated design process by using B-Splines and Subdivi-
sion surfaces, refer to [11,24]. In the framework presented
in this contribution we will adopt on isogeometric analy-
sis based on NURBS (Non-Uniform Rational B-Splines) as
introduced by Hughes et al. [22] with the aim to create a
link between the fields of geometric design (CAD-computer
aided design) and structural analysis (CAE-Computer aided
engineering). There are good reasons for that choice, namely
the fact that NURBS are the standard in most of today’s CAD
software and, for example, are able to exactly describe conic
sections. Isogeometric analysis has been successfully applied
to various fields of engineering, e.g. solid and shell mechan-
ics as well as computational fluid dynamics, and has shown
superior performance compared to standard finite elements,
see e.g. [2–6,14–16]. In our opinion, a promising approach
for a fully integrated system is the use of order-reduced struc-
tural models, e.g. membrane and shell elements where appli-
cable. With these models, thin-walled 3D structures, as they
are commonly present in the fields of mechanical, aeronauti-
cal, and civil engineering, can be computed and analysed in
an integrated isogeometric setting without any loss of infor-
mation as they only require a pure surface description. There
is a limitation associated with the NURBS-based isogeomet-
ric analysis, namely that the trimming method, as used in
most CAD software, creates surfaces which are not directly
applicable for the analysis. A possible remedy is to gener-
ate analysis-aware discrete structural models, e.g. a surface
composed out of several suitable patches. Recently, isogeo-
metric analysis with T-Splines was proposed, which might
overcome this general problem, see [1,17], but there still
remain open questions, e.g. the linear independence of the
T-Spline basis functions [10].
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R. Schmidt et al.
In this paper we present an integrated structural design
process where the analysis pipeline is combined with
the design process. During this procedure the geometric
information is preserved and at each step of the analysis
pipeline the geometric model is enhanced to the analysis
model. To accomplish this goal several issues, which are
due to the raised demands when integrating CAD and CAE,
are captured, resolved, and integrated in the presented struc-
tural design process. This includes general considerations
independent of the chosen element formulation and specific
problems concerning the applied shell element.
This paper is organized in the following way. In Sect. 2 the
integrated structural design process is presented. In Sect. 3
the required knowledge about NURBS and the nomenclature
is provided. Section 4 gives a brief but general introduction to
isogeometric analysis and information about the used shell
element. The section is concluded by remarks concerning
continuities. In the next section important facts about analy-
sis-aware modelling are provided. Section 6 gives a detailed
view on continuity considerations with respect to the inte-
grated structural design process. In Sect. 7 the developed
preprocessing tool for the isogeometric analysis, a Rhino
plug-in,1 is presented giving remarks concerning the bound-
ary conditions and illustrating the integrated design process
using an example. Concluding remarks and a general outlook
for the integration process of CAD and CAE are given in the
last section.
2 A mechanical view on the integrated design process
Every simulation of a realistic problem requires a precise
geometric modelling of the part of interest, which is mostly
done with CAD tools. For the analysis this model has to be
transferred to a CAE software and the geometric informa-
tion has to be translated into an analysis-compliant form.
This is realized by applying a geometric conversion (domain
discretisation), which is a geometrically irreversible trans-
formation and consequently introduces a geometrical error.
This is also often referred to mesh generation. The domain
discretisation has to be carefully generated since the mesh
quality is crucial for the validity of the results of the compu-
tations. Therefore, a lot of effort (and time) is put on the cre-
ation of suitable meshes, e.g. mesh optimization [21]. Since
a numerical method is applied and refinement procedures are
a common strategy to obtain a better approximation of the
solution, this has to be done for every refinement level. In
the standard process this requires a complete new setup of
the analysis model, i.e. restarting from the CAD model. The
standard structure of the interaction between CAD and CAE
is illustrated in Fig. 1.
1 www.rhino3d.com.
Fig. 1 Schematic structure of the common interaction between CAD
and CAE
Fig. 2 Schematic description of the structural design process where
CAD and CAE are encapsulated inside a single framework
In our opinion the description of the underlying geometry
with the same functions in both disciplines and the combi-
nation of modelling and preprocessing in the CAD environ-
ment are the steps towards a complete integrated system. This
is schematically visualized in Fig. 2. By applying the stan-
dard isogeometric concept within the analysis framework,
the connection of design and analysis is invoked. In this con-
text we assume that today’s design tools are mostly using
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