1. Design of a Light-Weight Mixed-Material Door
Through Structural Optimization
Anand Ramani Anshul Kaushik
Senior Researcher Researcher
Global General Motors R&D Global General Motors R&D
rd rd
Units 1-3, 3 Floor, Creator Units 1-3, 3 Floor, Creator
Bldg., ITPL, Whitefield Road, Bldg., ITPL, Whitefield Road,
Bangalore 560 037, INDIA Bangalore 560 037, INDIA
Abbreviations: SSTS – Sub-System Technical Specifications, HS – High Strength, LS – Low Strength, Al –
Aluminum, Mg – Magnesium
Keywords: Door, Light-weight, Topology Optimization
Abstract
Employing commonly considered design materials, a light-weight design of a door structure was arrived at through a sequence of
optimization studies. Starting from the performance requirements for various load cases specified in the SSTS, the methodology
combined topology and size optimization studies to obtain several design concepts with various material combinations for the door
outer, inner and header frame. Results from these studies established the relationship between the mass of untrimmed door structure
and the material composition of its design. Based on these results, one of the lightest concepts was chosen for additional study to
arrive at a potential design of the door structure, whose gauge thicknesses were further optimized, resulting in a light-weight design
that satisfies the SSTS performance requirements. The application of optimization methods and multi-material design resulted in about
46% mass reduction for the door structure compared to an all-steel design currently in use.
Introduction:
Light-weighting the body structure and closures with advanced materials and synthesis techniques is being
actively pursued in the automotive industry. Towards this, design concepts are being obtained and refined
using structural optimization methods. Various prior studies have focused on the light-weight design of
automotive structures. A comprehensive study in [1] on mass reduction opportunities in automotive body
structures using light-weight materials identified methods for reduction in the mass of closures and
estimated that about 20% to 40% mass savings can be obtained using currently available material
combinations and some niche materials that are currently not used for automotive design. This study
focused mainly on the material aspects of weight reduction. Other studies such as [2], [3] and [4] have also
explored the possibility of using light-weight materials to reduce the mass of automotive sub-components.
Similarly, several optimization studies on the door structure in the literature have considered simultaneous
topology and size optimization – for example, the use of tailor welded blanks in [5] and thickness
optimization in [6] – resulting in moderate mass savings (5 to 10%). It is expected that larger mass savings
can be obtained by combining multi-material design along with optimization techniques. The optimization
exercise needs to begin with topology optimization so that the design space is fully explored and the best
concept is chosen for converting to a final design. Also, the entire door needs to be considered as a total
structural system so that interaction effects between the components are exploited in obtaining the lightest
possible design, while satisfying the performance requirements for all the applicable load cases.
Simultaneously, the manufacturability of the design needs to be ascertained. These points are addressed
and demonstrated in the present methodology.
Process Methodology
The door structure of a rear door, typical of a large sedan, consists of the door outer, the door inner, its
reinforcements and the header. The door header is predominantly of frame construction with a hollow
prismatic section. The door is connected to the body through two door hinges. The design domain for
optimization was obtained from this door structure and consists of the outer, the header and the design
space for the inner as shown in Fig. 1. In addition, there is space for a layer of adhesive material between
the inner and the outer.
Finite Element Model Details: The finite element model of the door can be grouped into seven components
as described in Table I. Component meshes are shown in Fig. 1. Although a small slice of the design
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2. space of the inner is required for up-and-down movement of the glass window, this space was not removed
from the design region; instead the entire depth of the inner was considered as the design region. Two
kinds of element meshes were considered for the inner: (i) a solid mesh as shown in Fig. 1, and (ii) a lattice-
shell mesh which is obtained from the solid mesh by first extracting the faces of the solid elements and then
deleting all the duplicate shell elements and all the solid elements. The adhesive layer is modeled as a
single layer of solid elements sandwiched between the meshes of the outer and inner. Rigid links are used
to connect the mesh of the door outer to that of the inner at the hem-line as shown in Fig. 1. In addition,
rigid elements are also used to connect the hinges with the door inner and the latch with the door inner.
Normally, the header is connected to the door inner structure through header attachment brackets.
However, in the optimization model, the structure of the inner is not known a priori. Therefore, the header is
connected to the door inner structure through rigid links as shown in Fig. 1. The full door model with the
solid mesh of the door inner had 45561 elements and 45782 nodes. The full door model with the lattice-
shell mesh of the door inner had 104239 elements and 45782 nodes.
TABLE I
MODEL DETAILS
Thickness Number of optimization Number of design
# Component Mesh details
details solution cases variables
3 mm upper
2725 shell thickness
1 Door outer elements bound 5 (for 5 materials) 1 thickness variable
27426 solid
Door inner (solid mesh) elements 27426 topology variables
constant
thickness of 1
Door inner (lattice-shell 86002 shell mm for the
2 mesh) elements lattice-shells 5 (for 5 materials) 86002 topology variables
Upper and
lower thickness
bounds same
11622 shell as for door 1 (Material is the same 21 thickness variables for
3 Door header elements outer as for door inner) 21 sub-components
2725 solid 1 (material is not allowed
4 Adhesive layer elements to vary) 2725 topology variables
6 mm upper
and 0.7 mm 1 (made of HS steel.
835 shell lower thickness Material is not allowed to 4 thicknesses variables for
5 Door hinges elements bound vary) 4 sub-components
6 Rigid elements 1 None
Non-design elements
(elements in the connecting
regions with rigid elements) –
not considered for stress 1 (Material is the same
7 satisfaction as for door inner) None
30177 (in the case of solid
mesh for door inner)
88753 (in the case of
=5x5x1x1x1x1x1 lattice-shell mesh for door
Aggregated = 25 solution cases inner)
Load Cases and Boundary Conditions: From the sub-system technical specifications (SSTS), load cases
with performance criteria based on structural stiffness, deflections, stresses and natural frequencies were
considered for the optimization study. These were: vertical, torsional and header (hinge pillar and lock
pillar) rigidity, inner and outer belt-line stiffness, quasi-static stiffness, fundamental frequency and the door
inner panel attachment interface stiffness load cases. Stress limits were imposed for the vertical rigidity,
belt-line stiffness and quasi-static stiffness load cases and corresponded to the yield strength of the chosen
material. Durability load cases and load cases pertaining to attachment sub-systems were not considered
for optimization. Further, non-linear and dynamic load cases were not part of the initial optimization study
because of limitations imposed by the optimization software.
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3. FIGURE 1: FINITE ELEMENT MODEL DETAILS
Materials Considered: The materials considered for optimization were steel, aluminum ( (Al) and magnesium
(Mg). For steel and Al, two material grades – high strength (HS) and low strength (
, (LS) – were considered.
These were chosen so as to span the range of real material grades with representative values for the
material yield strength, in order to study its effect on the optimization results. Properties of all these
materials are shown in Table II. A Poisson’s ratio of 0.3 was used for metals and a value of 0.36 was used
.
for the adhesive.
TABLE II
MATERIAL PROPERTIES
Elastic Yield Minimum
Density
# Material modulus Strength thickness
(kg/m3)
(x 1011 N/m2) (MPa) (mm)
1 LS steel 2.1 7800 350 0.8
2 HS steel 2.1 7800 1000 0.7
3 LS Al 0.7 2630 100 1.1
4 HS Al 0.7 2630 250 1.1
0.44 1740 125 1.25
5 Mg
0.014 1100 Not used -
6 Adhesive
Design Variables for Optimization and Optimization Solution Cases: The design variables considered for
optimization were based on the grouping of components as described in Table I. It can be observed that the
t
number of material choices considered for each component and the manner in which the material choices
were linked between various components resulted in 25 optimization solution cases. Since two modeling
options were considered for the door inner (solid mesh and lattice shell mesh), this resulted in a total of 50
oor lattice-shell
solution cases.
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4. Results And Discussions
®
The software OptiStruct ver. 10.0 (2010) was used to solve the optimization problem. Solution turn
turn-around
times were approximately eight hours for the model with the solid mesh of the inner and 15 hours for the
model with the lattice mesh of the inner. The simulations were performed on a desktop work
d work-station with a
12 GB RAM, 2.27 GHz CPU and running a 64 64-bit MS-Windows 7 operating system.
Mass Variation: Results from all the optimization runs were aggregated into tabular data and are plotted in
Fig. 2, which shows the mass from the optimization solutions plotted against the material combinations for
the door inner and outer, for both the models of the door inner – the solid mesh and the lattice shell mesh. It
is apparent that the mass trends for both these cases are similar and the model with the lattice mesh for the
are
inner resulted in lower masses. Because of the potential of the lattice shell model to yield light
lattice-shell light-weight
designs, further discussion of results is focused on the simulations which employed this model of the door
employed
inner. It can be observed that the total mass of the door ranges between 12.4 kg for the LS steel outer and
inner to 5.95 kg for the Mg outer and inner. From practical considerations, since Mg cannot yet be used to
manufacture Class-A surfaces for the outer, the next lightest option is one with a HS Al outer and a Mg
s
inner, which weighs 6.35 kg. From Fig. 2, i can also be observed that irrespective of the material for the
it
outer, the mass variation with the material for the inner is nearly constant at about 4.25 kg. The mass
constant
variation with outer material is in the range of 2.7 to 3.1 kg, or 2.9 kg on average. For the all-steel design,
the mass variation from a LS steel inner and outer to a HS steel inner and outer is about 0.7 kg. This
difference reduces to a marginal value of about 0.1 kg for an all
erence all-Al design, indicating th the material
that
strength has an insignificant effect on the design mass when lighter materials are considered.
FIGURE 2: MASS PLOT FROM THE OPTIMIZATION SOLUTIONS
Obtaining the Final Design: Since there are a few topology solutions with only small differences in mass,
other criteria such as manufacturing and cost were used to select a potential concept for further
development. Thus, the concept with LS Al outer an Mg inner and header with a total mass of 6.41 kg was
and
chosen for obtaining the final design Space was made for up-and-down movement of the window glass
design. down
and the optimization solution was re
re-obtained. The new mass was lower at 6.06 kg (compared to 6.41 kg
obtained previously) and is evidence of the presence of multiple-optima for such problems. The resulting
optima
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5. topology for the inner had a preponderance of latticed features which implied that it was difficult to
manufacture. Hence, additional lattice thicknesses of 1.5 and 2 mm were considered and topology
optimization solutions were re-obtained, yielding masses of 6.38 and 6.8 kg respectively. The mass
increases with increasing lattice thickness, but the preponderance of latticed features decreases, as can be
seen in Fig. 3. For the 2 mm lattice thickness, the topology had minimal lattice content and was hence
chosen for creating the final design. The design of the door inner was constructed from the topology density
contours, as shown in Fig. 4. The design mesh of the inner had 8092 shell elements. A layer of solid
elements with adhesive material running along the hem-line was used to connect the inner and the outer.
Element-wise and zone-wise (by dividing the mesh into a number of zones) thickness optimization for the
shell elements of the inner were considered with thickness bounds of (1.25, 5) mm. Both options were
combined with the thickness optimization of the door outer, header and hinges as in Table I. Slightly
different masses were obtained in each case. Final optimization iterations were performed after including
the crash beam (additional thickness variable) and the fixed glass holder, which were not included in the
original model. The thickness of the crash beam was not varied, as it was to be determined from crash
simulations. The final mass obtained was 7.12 kg and can be considered to be the final minimum-mass
design of the door structure, confirming that a light-weight design with almost the same mass as that
obtained from topology optimization can be obtained by starting with the topology concept. The design thus
obtained was also verified for its performance in nonlinear load cases like nonlinear deflection, dent
resistance and oil-canning. The final design of the door inner can be manufactured by a casting process.
Benefits Summary
Compared to a structure that was designed without recourse to optimization techniques, and instead
optimized by conventional trial-and-error modification, about 1.5 kg reduction in mass (17%) was achieved.
Compared with an all-steel door structure, the mass reduction from a multi-material design optimization with
light-weight materials is about 6.1 kg (46%).
Challenges
Availability of multi-material and multi-thickness topology optimization, robustness of the optimization
algorithm, ability to optimize for nonlinear and dynamic load cases, obtaining clear black-and-white solutions
instead of density contours, etc. can significantly improve design productivity and the quality of the final
designs. Methods to address these issues are currently being developed in GM.
Future Plans
The results obtained in the present study encourage a more comprehensive effort in creating a practical
light-weight door structure using an Al outer and a cast-Mg inner. Additional manufacturing considerations
(such as the spacing and thickness of ribs in the inner, attachment of the header to inner, etc.) need to be
accounted for in this exercise so as to obtain a practical design. Also, performance in other load cases
which involve interaction with the body-in-white (such as door check durability, side impact requirements,
etc.) need to be verified and the design modified accordingly. These will form part of future work.
Conclusions
Following the process of topology optimization and subsequent gauge optimization, the minimum-mass
multi-material design of the untrimmed rear door structure was determined to be about 7.1 kg, which is
about 17% less than one obtained using conventional methods of design, without recourse to optimization
tools. It has been demonstrated that proper use of multi-material synthesis and optimization techniques
starting from topology optimization can result in light-weight designs. Further improvements in optimization
methods can enhance design productivity and the quality of the final designs.
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6. FIGURE 3: TOPOLOGIES OF THE DOOR INNER FOR VARIOUS LATTICE SHELL THICKNESSES
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7. FIGURE 4: FINAL DESIGN OF THE DOOR INNER
ACKNOWLEDGEMENTS
The authors would like to thank Anil Sachdev James O’Kane, Naveen Shankar (EASI Engineering),
Sachdev,
Santosh Swamy, Umesh Nayaka, Shunmugam Bhaskar, Rinaldo Lucchesi, Arnoldo Garcia Kouichi Inaba,
Garcia,
Prakash Mangalgiri, Narendran Balan and Prabhakar Marur for their inputs, help and reviews
lgiri, reviews.
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Journal
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