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UNDER THE GUIDANCE OF
PRESENTED BY
VISHAL AGARWAL
212111406
M.TECH STRUCTURAL ENGINEERING 2021-2023
INTRODUCTION
• Monolithic Dome is thin wall reinforced concrete shell structure.
• A monolithic dome (from Greek mono and lithic meaning "one stone") is a
structure cast in a one-piece form.
• The structure provides safe shelter for the people area with
hurricanes,fires,bomb blasts and earthquakes.
• Domes belong to the category of self supporting structures that take
the form of an arch. They distribute loads around the sides and down the
foundation.
• A curve rotated about a central axis to form a surface, creates a DOME.
• The shape of the dome depends upon the type of the curve and the
direction of the axis of revolution.
2
MONOLITHIC DOME
3
Dome of a Home Survived
Hurricane Ivan on September 16, 200
Texas , USA
Literature review
Disaster Survivability of Thin-Shell Concrete Dome
Structures: Experience and Practice
Andrew South AUTHOR*, Chris ZWEIFELa * Department of Civil and
Environmental Engineering, Stanford University
Proceedings of the IASS-SLTE 2014 Symposium
•concrete thin-shell domes produce envelope shell
sections sufficient to withstand loads produced in
extreme natural disasters.
•Implications for practitioners suggest that as disaster
resistant design criteria for various structures
continues to become increasingly important to
governments, communities and building owners, thin-
shell concrete structures (such as air-formed dome
structures) are a potentially under-utilized envelope
system where practical design approaches inherently
produce structures capable of withstanding extreme
5
6
 MONOLITHIC DOMES ARE CONSTRUCTED FOLLOWING A METHOD THAT
REQUIRES A TOUGH, INFLATABLE AIRFORM, STEEL-REINFORCED
CONCRETE AND A POLYURETHANE FOAM INSULATION. EACH OF THESE
INGREDIENTS IS USED IN A TECHNOLOGICALLY SPECIFIC WAY.
STEP BY STEP PROCEDURE :
1. FOUNDATION
2. AIRFORM
3. POLYURETHANE FOAM
4. STEEL REBAR
5. SHOTCRETE
CONSTRUCTION TECHNIQUE
Step 1- Excavation Step 2- Foundation +
placing of balloon
Step 3- Inflating balloon
Step 3- Inflating balloon Step 4- Formwork for windows Step 5- Rebaring
Step 5- Rebaring Step 6- Services-Electrical
& Plumbing
Step 6- Services-
Electrical & Plumbing
Step 7- Shortcreting Step 8- Curing Step 9- Marking for interiors
Step 10- Partition walls Step 11- Laying Slabs
Step 12- Stairs Step 13- Laying fixtures Step 14- Interior Finishing
Literature review
The impact of diameter, number of ribs, percentage of steel,
compressive strength and cover thickness on the large concrete
dome Dr. Hani Aziz Ameen
Asst. Prof., Pumps Engineering Department - Technical College / Al-Musaib – Iraq
Am. J. Sci. Ind. Res., 2010, 1(3): 472-495
Based on the present finite element model by ANSYS12, a parametric
study was performed to investigate the influence of several important
parameters on the behavior of concrete dome
Load deflection at crown by different diameter
Load deflection at crown by different grade of conc
Load deflection at crown by different %
Load deflection at crown by different cover
thickness
DOME PROFILES
 Lower the profile the less expense.
 Windows and doors on the second floor can be
augmented.
 If the land is a premium, go up with integrated
stem wall.
11
12
Various shapes of monolithic domes
LITERATURE REVIEW
Shape optimization of shell structures Ekkehard
Ramm* - Kai-Uwe Bletzinger** -Reiner Reitinger***
'The paper was originally published in the bulletin of the International
Association for Shell and Spatial Structures, Vol. 34 (1993) n° 2“
The methods of structural optimization have been presented as
general computational tools to find the shape of shells subjected to
many different combinations of objectives and constraints.
SHAPES
DOME VARIATIONS/CONFIGURATIONS
a) Low profile spherical segment :
 Most efficient shape.
 Used for large domes.
b) Hemisphere :
 Surface area is double the floor area.
 Useful for high-volume storage buildings
and smaller structures ,such as homes
c) High profile spherical segment :
 Most volume for the least floor area.
 Used for water tanks, storage buildings,
homes etc..
14
e) Prolate ellipsoid (Long axis
horizontal):
 Elliptical base creates a very unique
space
f) Prolate ellipsoid (Long axis vertical) :
 It is very tall.
 Useful for bulk storage and buried
building.
g) Torus :
 Not as space -efficient as dome.
 These are homes with a centre
courtyard or garden.
15
LITERATURE REVIEW
Acoustic of monolithic dome structures
Mostafa Refat Ismail, Hazem Eldalyn Department of Architecture
Engineering, Faculty of Engineering, Ain Shams University, Egypt
Frontiers of Architectural Research (2018) 7, 56–66
This study discussed issues related to acoustic design strategies
of residential monolithic dome structures and outlined mitigation
measures to the concentration of sound energy caused by
complex internal concave surfaces.
•By introducing absorptive materials to the internal upper cap of
the monolithic dome structure, the critical sound components
reflected by the upper exposed shell of the dome are absorbed
and the focusing of sound energy is minimized in these small
residential units.
STRESSES ACTING ON DOMES
 Generally, a spherical dome may be imagining consisting of a number of
horizontal rings placed one over the other.
 The diameters of the successive rings increase in the downward direction and the
equilibrium is maintained independently of the rings above it.
 The circle of each ring is called latitude while the circle drawn through two
diametrically opposite points on a horizontal diameter and the crown is known as
a meridian circle.
 The entire meridian circles coverage at the crown of the spherical dome.
Two types of stresses acting on the domes are :
 Meridian thrust (T) along the direction of meridian
 Hoop stress along latitudes
18
19
LITERATURE REVIEW
Design and Analysis of Monolithic Dome Structure
Rahul Ingale1 Amol Dighe2 Vaibhav Badhe3 Girjinath Damale4
Prof. Pote R.K.5
(IJSRD/Vol. 6/Issue 04/2018/021)
concluded that the results obtained by manual design and
Software design STAAD PRO V8i are approximately equals
and also very nominal reinforcement required to construct
the monolithic dome structure. Hence the monolithic dome
building technique is an effective alternative to conventional
method
DOME OPENINGS
 If dome is not huge, then all kinds of openings are possible.
 Stresses are higher in domes having diameter larger than
100 feet.
 Build the openings for the uses.
23
ADVANTAGES
Advantages of a monolithic dome fall into three general categories :
a) Economy in construction :
 Cost of a dome is less .
 Streamlined construction process and use of only four ingredients contribute
to the domes economy.
 Require less maintenance.
b) Security :
 Ability to survive tornadoes, hurricanes and earthquakes.
 Provides fire protection.
 They are very good for circulation of air and heat so they are also for very
cold climates.
c) comfort :
 Any structure appears bare and unattractive when its first built.
 But just as enhancement can soften and beautify straight lines and corners.
24
LITERATURE REVIEW
Analysis and Design of Monolithic Domes for Low Cost
Housing 1Kalaiselvi M, 2 Selvakumar T, 3 Padmasri .G
IJEDR 2018 | Volume 6, Issue 3 | ISSN: 2321-9939
COST ESTIMATION The detailed cost estimation of normal
conventional building and monolithic concrete dome housing of
same size are compared
DISADVANTAGES
Disadvantages of monolithic dome :
a)Engineering :
 Only specially trained construction crews. Using the modern
techniques.
 Wasted space in narrow corners.
 Lack of seams.
b)Social :
 Different appearance of the domes decreases the appeal for their
use as private residences and the strange appearance and design
may run afoul of neighbourhood building covenants..
 Building permits may be difficult to obtain if local officials are not
familiar with the monolithic dome.
 Resale of a monolithic dome home may be difficult because of its
unconventional appearance.
26
LITERATURE REVIEW
A STUDY IN MONOLITHIC STRUCTURE
1NIKITA PATEL, 2NAMRATA VERMA
International Journal of Mechanical And Production
Engineering, ISSN: 2320-2092, Volume- 5, Issue-11, Nov.-2017
In ancient times domes are very popular because of its uniqueness in
providing maximum space area with minimum surface area requirement
but because of its high supervision requirement, tedious work process &
invention of an advantageous method of construction, its popularity gets
reduces. So we have to try to make it easier than older one, some
possible future aspects of domes evaluated; two prominent are
MONOLITHIC DOMES & GEODESIC DOMES
Dome have been used in development of silos, residential building,
school& stadium, roof of industries, nuclear reactor, pressure vessel,
auditorium because it is capable of providing safe area, minimum
material, easy to erect, heat efficient, membrane action & enable to
absorb very large loads with a small thickness.
Typical schematic plan and section of a monolithic dome
residential unit showing various radius
In 2000,
Catalytic
Software
began the
construction of
a massive, self-
sustaining
complex of
domes, that
includes
attractive, safe
areas for living,
working and
socializing.
New Oroville is
designed to
provide all that
the suburban life
offers, such as
parks, gardens,
swimming pools,
clean water and
more.
In this high-tech society, every
employee will live in a one-,
two- or three-story dome home
that has the ability to withstand
natural disasters and is
equipped with lightning speed
Internet access.
New Oroville is located
on 50 acres in
Hyderabad, India’s high-
tech hub, and includes
some 4000 domes.
New Oroville was designed for
superior protection. The domes act
as information silos, physically
separating teams and isolating
data.
The eco-friendly domes are
durable and energy efficient.
To make the construction process more
efficient, local labor crews were divided
into four categories: Mixer Crew, Spray
Crew, Steel Crew and Form Crew.
1. Sustainability Monolithic Domes have real strength. They can
withstand the force of a tornado, hurricane or earthquake. Their
lifespan is measured in centuries. Hence they do not need to be
replaced.
2. Energy Efficiency The Monolithic Dome is energy efficient. It will
usually save fifty percent on heating and cooling costs compared to a
comparable conventional building.
3. Green Materials Owing much to their design, Monolithic Domes
require the smallest surface area and employ the fewest materials to
enclose space. A dome, will always use less material (generally 50% to
75% less) to cover the same space utilized by a ‘square’ conventional
building. Less material means less cost, or higher quality materials for
the same cost, or both.
CONCLUSION
REFERNCES
1. Acoustic of monolithic dome structures Mostafa Refat Ismail, Hazem Eldalyn Department of
Architecture Engineering, Faculty of Engineering, Ain Shams University, Egypt
2. A CRITICAL LITERATURE REVIEW ON COMPARATIVE STUDY OF CONVENTIONAL
STRUCTURE WITH MONOLITHIC STRUCTURE Devang Gohel1 , Dr. Jayeshkumar
Pitroda2 , | ISSN: 2320-2882
3. The impact of diameter, number of ribs, percentage of steel, compressive strength and cover
thickness on the large concrete dome Dr. Hani Aziz Ameen AMERICAN JOURNAL OF
SCIENTIFIC AND INDUSTRIAL RESEARCH doi:10.5251/ajsir.2010.1.3.472.495
4. Analysis and Design of Monolithic Domes for Low Cost Housing 1Kalaiselvi M, 2
Selvakumar T, 3 Padmasri .G © IJEDR 2018 | Volume 6, Issue 3 | ISSN: 2321-9939
5. Design and Analysis of a Monolithic Dome using Staadpro V8i - Review Rashmi C
Khanorkar1, Prathmesh S Narkar . IRJET | e-ISSN: 2395-0056
6. Design and Analysis of Monolithic Dome Structure Rahul Ingale1 Amol Dighe2 Vaibhav
Badhe3 Girjinath Damale4 Prof. Pote R.K.5 IJSRD | Vol. 6, Issue 04, 2018 | ISSN (online):
2321-0613
7. IS 2204 (1962): Code of practice for construction of reinforced concrete shell roof
7.Bureau of Indian Standards: IS-875 part 1
8.Analysis and design of the general and outmost-ring stiffened suspen-dome structures
Wenjiang Kang a , Zhihua Chen a , Heung-Fai Lam b,∗, Chenran Zuo a a Department of
Civil Engineering, Tianjin University, Tianjin, China
9. Disaster Survivability of Thin-Shell Concrete Dome Structures
Andrew South AUTHOR*, Chris ZWEIFELa * Department of Civil and Environmental
Engineering, Stanford University Proceedings of the IASS-SLTE 2014 Symposium
10. Shape optimization of shell structures Ekkehard Ramm* - Kai-Uwe
Bletzinger** -Reiner Reitinger***
'The paper was originally published in the bulletin of the International Association
for Shell and Spatial Structures, Vol. 34 (1993) n° 2“
monolithic dome structures

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monolithic dome structures

  • 1. UNDER THE GUIDANCE OF PRESENTED BY VISHAL AGARWAL 212111406 M.TECH STRUCTURAL ENGINEERING 2021-2023
  • 2. INTRODUCTION • Monolithic Dome is thin wall reinforced concrete shell structure. • A monolithic dome (from Greek mono and lithic meaning "one stone") is a structure cast in a one-piece form. • The structure provides safe shelter for the people area with hurricanes,fires,bomb blasts and earthquakes. • Domes belong to the category of self supporting structures that take the form of an arch. They distribute loads around the sides and down the foundation. • A curve rotated about a central axis to form a surface, creates a DOME. • The shape of the dome depends upon the type of the curve and the direction of the axis of revolution. 2
  • 3. MONOLITHIC DOME 3 Dome of a Home Survived Hurricane Ivan on September 16, 200 Texas , USA
  • 4. Literature review Disaster Survivability of Thin-Shell Concrete Dome Structures: Experience and Practice Andrew South AUTHOR*, Chris ZWEIFELa * Department of Civil and Environmental Engineering, Stanford University Proceedings of the IASS-SLTE 2014 Symposium •concrete thin-shell domes produce envelope shell sections sufficient to withstand loads produced in extreme natural disasters. •Implications for practitioners suggest that as disaster resistant design criteria for various structures continues to become increasingly important to governments, communities and building owners, thin- shell concrete structures (such as air-formed dome structures) are a potentially under-utilized envelope system where practical design approaches inherently produce structures capable of withstanding extreme
  • 5. 5
  • 6. 6  MONOLITHIC DOMES ARE CONSTRUCTED FOLLOWING A METHOD THAT REQUIRES A TOUGH, INFLATABLE AIRFORM, STEEL-REINFORCED CONCRETE AND A POLYURETHANE FOAM INSULATION. EACH OF THESE INGREDIENTS IS USED IN A TECHNOLOGICALLY SPECIFIC WAY. STEP BY STEP PROCEDURE : 1. FOUNDATION 2. AIRFORM 3. POLYURETHANE FOAM 4. STEEL REBAR 5. SHOTCRETE CONSTRUCTION TECHNIQUE
  • 7. Step 1- Excavation Step 2- Foundation + placing of balloon Step 3- Inflating balloon Step 3- Inflating balloon Step 4- Formwork for windows Step 5- Rebaring Step 5- Rebaring Step 6- Services-Electrical & Plumbing Step 6- Services- Electrical & Plumbing
  • 8. Step 7- Shortcreting Step 8- Curing Step 9- Marking for interiors Step 10- Partition walls Step 11- Laying Slabs Step 12- Stairs Step 13- Laying fixtures Step 14- Interior Finishing
  • 9. Literature review The impact of diameter, number of ribs, percentage of steel, compressive strength and cover thickness on the large concrete dome Dr. Hani Aziz Ameen Asst. Prof., Pumps Engineering Department - Technical College / Al-Musaib – Iraq Am. J. Sci. Ind. Res., 2010, 1(3): 472-495 Based on the present finite element model by ANSYS12, a parametric study was performed to investigate the influence of several important parameters on the behavior of concrete dome Load deflection at crown by different diameter Load deflection at crown by different grade of conc
  • 10. Load deflection at crown by different % Load deflection at crown by different cover thickness
  • 11. DOME PROFILES  Lower the profile the less expense.  Windows and doors on the second floor can be augmented.  If the land is a premium, go up with integrated stem wall. 11
  • 12. 12 Various shapes of monolithic domes
  • 13. LITERATURE REVIEW Shape optimization of shell structures Ekkehard Ramm* - Kai-Uwe Bletzinger** -Reiner Reitinger*** 'The paper was originally published in the bulletin of the International Association for Shell and Spatial Structures, Vol. 34 (1993) n° 2“ The methods of structural optimization have been presented as general computational tools to find the shape of shells subjected to many different combinations of objectives and constraints.
  • 14. SHAPES DOME VARIATIONS/CONFIGURATIONS a) Low profile spherical segment :  Most efficient shape.  Used for large domes. b) Hemisphere :  Surface area is double the floor area.  Useful for high-volume storage buildings and smaller structures ,such as homes c) High profile spherical segment :  Most volume for the least floor area.  Used for water tanks, storage buildings, homes etc.. 14
  • 15. e) Prolate ellipsoid (Long axis horizontal):  Elliptical base creates a very unique space f) Prolate ellipsoid (Long axis vertical) :  It is very tall.  Useful for bulk storage and buried building. g) Torus :  Not as space -efficient as dome.  These are homes with a centre courtyard or garden. 15
  • 16. LITERATURE REVIEW Acoustic of monolithic dome structures Mostafa Refat Ismail, Hazem Eldalyn Department of Architecture Engineering, Faculty of Engineering, Ain Shams University, Egypt Frontiers of Architectural Research (2018) 7, 56–66 This study discussed issues related to acoustic design strategies of residential monolithic dome structures and outlined mitigation measures to the concentration of sound energy caused by complex internal concave surfaces. •By introducing absorptive materials to the internal upper cap of the monolithic dome structure, the critical sound components reflected by the upper exposed shell of the dome are absorbed and the focusing of sound energy is minimized in these small residential units.
  • 17.
  • 18. STRESSES ACTING ON DOMES  Generally, a spherical dome may be imagining consisting of a number of horizontal rings placed one over the other.  The diameters of the successive rings increase in the downward direction and the equilibrium is maintained independently of the rings above it.  The circle of each ring is called latitude while the circle drawn through two diametrically opposite points on a horizontal diameter and the crown is known as a meridian circle.  The entire meridian circles coverage at the crown of the spherical dome. Two types of stresses acting on the domes are :  Meridian thrust (T) along the direction of meridian  Hoop stress along latitudes 18
  • 19. 19
  • 20. LITERATURE REVIEW Design and Analysis of Monolithic Dome Structure Rahul Ingale1 Amol Dighe2 Vaibhav Badhe3 Girjinath Damale4 Prof. Pote R.K.5 (IJSRD/Vol. 6/Issue 04/2018/021) concluded that the results obtained by manual design and Software design STAAD PRO V8i are approximately equals and also very nominal reinforcement required to construct the monolithic dome structure. Hence the monolithic dome building technique is an effective alternative to conventional method
  • 21.
  • 22.
  • 23. DOME OPENINGS  If dome is not huge, then all kinds of openings are possible.  Stresses are higher in domes having diameter larger than 100 feet.  Build the openings for the uses. 23
  • 24. ADVANTAGES Advantages of a monolithic dome fall into three general categories : a) Economy in construction :  Cost of a dome is less .  Streamlined construction process and use of only four ingredients contribute to the domes economy.  Require less maintenance. b) Security :  Ability to survive tornadoes, hurricanes and earthquakes.  Provides fire protection.  They are very good for circulation of air and heat so they are also for very cold climates. c) comfort :  Any structure appears bare and unattractive when its first built.  But just as enhancement can soften and beautify straight lines and corners. 24
  • 25. LITERATURE REVIEW Analysis and Design of Monolithic Domes for Low Cost Housing 1Kalaiselvi M, 2 Selvakumar T, 3 Padmasri .G IJEDR 2018 | Volume 6, Issue 3 | ISSN: 2321-9939 COST ESTIMATION The detailed cost estimation of normal conventional building and monolithic concrete dome housing of same size are compared
  • 26. DISADVANTAGES Disadvantages of monolithic dome : a)Engineering :  Only specially trained construction crews. Using the modern techniques.  Wasted space in narrow corners.  Lack of seams. b)Social :  Different appearance of the domes decreases the appeal for their use as private residences and the strange appearance and design may run afoul of neighbourhood building covenants..  Building permits may be difficult to obtain if local officials are not familiar with the monolithic dome.  Resale of a monolithic dome home may be difficult because of its unconventional appearance. 26
  • 27. LITERATURE REVIEW A STUDY IN MONOLITHIC STRUCTURE 1NIKITA PATEL, 2NAMRATA VERMA International Journal of Mechanical And Production Engineering, ISSN: 2320-2092, Volume- 5, Issue-11, Nov.-2017 In ancient times domes are very popular because of its uniqueness in providing maximum space area with minimum surface area requirement but because of its high supervision requirement, tedious work process & invention of an advantageous method of construction, its popularity gets reduces. So we have to try to make it easier than older one, some possible future aspects of domes evaluated; two prominent are MONOLITHIC DOMES & GEODESIC DOMES Dome have been used in development of silos, residential building, school& stadium, roof of industries, nuclear reactor, pressure vessel, auditorium because it is capable of providing safe area, minimum material, easy to erect, heat efficient, membrane action & enable to absorb very large loads with a small thickness.
  • 28. Typical schematic plan and section of a monolithic dome residential unit showing various radius
  • 29. In 2000, Catalytic Software began the construction of a massive, self- sustaining complex of domes, that includes attractive, safe areas for living, working and socializing. New Oroville is designed to provide all that the suburban life offers, such as parks, gardens, swimming pools, clean water and more. In this high-tech society, every employee will live in a one-, two- or three-story dome home that has the ability to withstand natural disasters and is equipped with lightning speed Internet access.
  • 30. New Oroville is located on 50 acres in Hyderabad, India’s high- tech hub, and includes some 4000 domes. New Oroville was designed for superior protection. The domes act as information silos, physically separating teams and isolating data. The eco-friendly domes are durable and energy efficient. To make the construction process more efficient, local labor crews were divided into four categories: Mixer Crew, Spray Crew, Steel Crew and Form Crew.
  • 31.
  • 32.
  • 33.
  • 34. 1. Sustainability Monolithic Domes have real strength. They can withstand the force of a tornado, hurricane or earthquake. Their lifespan is measured in centuries. Hence they do not need to be replaced. 2. Energy Efficiency The Monolithic Dome is energy efficient. It will usually save fifty percent on heating and cooling costs compared to a comparable conventional building. 3. Green Materials Owing much to their design, Monolithic Domes require the smallest surface area and employ the fewest materials to enclose space. A dome, will always use less material (generally 50% to 75% less) to cover the same space utilized by a ‘square’ conventional building. Less material means less cost, or higher quality materials for the same cost, or both. CONCLUSION
  • 35. REFERNCES 1. Acoustic of monolithic dome structures Mostafa Refat Ismail, Hazem Eldalyn Department of Architecture Engineering, Faculty of Engineering, Ain Shams University, Egypt 2. A CRITICAL LITERATURE REVIEW ON COMPARATIVE STUDY OF CONVENTIONAL STRUCTURE WITH MONOLITHIC STRUCTURE Devang Gohel1 , Dr. Jayeshkumar Pitroda2 , | ISSN: 2320-2882 3. The impact of diameter, number of ribs, percentage of steel, compressive strength and cover thickness on the large concrete dome Dr. Hani Aziz Ameen AMERICAN JOURNAL OF SCIENTIFIC AND INDUSTRIAL RESEARCH doi:10.5251/ajsir.2010.1.3.472.495 4. Analysis and Design of Monolithic Domes for Low Cost Housing 1Kalaiselvi M, 2 Selvakumar T, 3 Padmasri .G © IJEDR 2018 | Volume 6, Issue 3 | ISSN: 2321-9939 5. Design and Analysis of a Monolithic Dome using Staadpro V8i - Review Rashmi C Khanorkar1, Prathmesh S Narkar . IRJET | e-ISSN: 2395-0056 6. Design and Analysis of Monolithic Dome Structure Rahul Ingale1 Amol Dighe2 Vaibhav Badhe3 Girjinath Damale4 Prof. Pote R.K.5 IJSRD | Vol. 6, Issue 04, 2018 | ISSN (online): 2321-0613 7. IS 2204 (1962): Code of practice for construction of reinforced concrete shell roof
  • 36. 7.Bureau of Indian Standards: IS-875 part 1 8.Analysis and design of the general and outmost-ring stiffened suspen-dome structures Wenjiang Kang a , Zhihua Chen a , Heung-Fai Lam b,∗, Chenran Zuo a a Department of Civil Engineering, Tianjin University, Tianjin, China 9. Disaster Survivability of Thin-Shell Concrete Dome Structures Andrew South AUTHOR*, Chris ZWEIFELa * Department of Civil and Environmental Engineering, Stanford University Proceedings of the IASS-SLTE 2014 Symposium 10. Shape optimization of shell structures Ekkehard Ramm* - Kai-Uwe Bletzinger** -Reiner Reitinger*** 'The paper was originally published in the bulletin of the International Association for Shell and Spatial Structures, Vol. 34 (1993) n° 2“