Abstract
This paper gives an overview of the factors that affect the strength and structural design of advanced thin-walled marine structures with reduced plate thickness or alternative topologies to those used today in the marine industry. Due to production-induced initial deformations and resulting geometrical non-linearity, the classical division between primary, secondary, and tertiary responses becomes strongly coupled. Volume-averaged, non-linear response of structural element can be used to define the structural stress–strain relation that enables analysis at the next, larger, length scale. This, today’s standard homogenization process, needs to be complemented with localization, where the stresses are assessed at the details, such as welds for fatigue analysis. Due to this, the production-induced initial distortions need to be considered with high accuracy. Another key question is the length-scale interaction in terms of continuum description. Non-classical continuum mechanics are needed when consecutive scales are close. Strain-gradients are used to increase the accuracy of the kinematical description of beams, plates, and shells. The paper presents examples of stiffened and sandwich panels covering limit states such as fatigue, non-linear buckling, and fracture.
References
1.
Caldwell
, J. B.
, 1965
, “Ultimate Longitudinal Strength
,” Trans. RINA
, 107
, pp. 411
–430
.2.
Faulkner
, D.
, 1975
, “A Review of Effective Plating for the Analysis of Stiffened Plating in Bending and Compression
,” J. Ship Res.
, 19
(1
), pp. 1
–17
.3.
Smith
, C. S.
, 1977
, “Influence of Local Compressive Failure on Ultimate Longitudinal Strength of a Ship’s Hull
,” Proceedings of the 1st International Conference on Practical Design of Ships and Other Floating Structures
, PRADS
, Tokyo
, Oct. 18–20
, pp. 73
–79
.4.
Dow
, R. S.
, Hugill
, R. C.
, Clark
, J. D.
, and Smith
, C. S.
, 1981
, “Evaluation of Ultimate Ship Hull Strength
,” Extreme Loads Response Symposium
, Arlington, VA
, Oct. 19–20
, SNAME
, pp. 133
–148
.5.
Guedes Soares
, C.
, and Søreide
, T. H.
, 1983
, “Behaviour and Design of Stiffened Plates Under Predominantly Compressive Loads
,” Int. Shipbuild. Prog.
, 30
(341
), pp. 13
–27
. 10.3233/ISP-1983-30341036.
Gordo
, J. M.
, and Guedes Soares
, C.
, 1996
, “Approximate Methods to Evaluate the Hull Girder Collapse Strength
,” Mar. Struct.
, 9
(3
), pp. 449
–470
. 10.1016/0951-8339(95)00030-57.
Paik
, J. K.
, Thayamballi
, A. K.
, and Jung
, S. C.
, 1996
, “Ultimate Strength of Ship Hulls Under Combined Vertical Bending, Horizontal Bending, and Shearing Forces
,” Trans. SNAME
, 104
, pp. 31
–59
.8.
Sadovský
, Z.
, Teixeira
, A. P.
, and Guedes Soares
, C.
, 2006
, “Degradation of the Compressive Strength of Square Plates Due to Initial Deflection
,” J. Constr. Steel Res.
, 43
(1
), pp. 369
–377
. 10.1016/j.jcsr.2005.07.0139.
Paik
, J. K.
, 2008
, “Some Recent Advances in the Concepts of Plate-Effectiveness Evaluation
,” Thin Walled Struct.
, 46
(7–9
), pp. 1035
–1046
. 10.1016/j.tws.2008.01.02210.
Xu
, M. C.
, and Guedes Soares
, C.
, 2012
, “Assessment of the Ultimate Strength of Narrow Stiffened Panel Test Specimens
,” Thin Walled Struct.
, 55
(1
), pp. 11
–21
. 10.1016/j.tws.2012.02.00611.
Xu
, M. C.
, and Guedes Soares
, C.
, 2013
, “Comparisons of Calculations With Experiments on the Ultimate Strength of Wide Stiffened Panels
,” Mar. Struct.
, 31
(1
), pp. 82
–101
. 10.1016/j.marstruc.2013.01.00312.
Geers
, M. G. D.
, Kouznetsova
, V. G.
, and Brekelmans
, W. A. M.
, 2010
, “Multi-Scale Computational Homogenization: Trends and Challenges
,” J. Comput. Appl. Math.
, 234
(7
), pp. 2175
–2182
. 10.1016/j.cam.2009.08.07713.
Miehe
, C.
, Schröder
, J.
, and Becker
, M.
, 2002
, “Computational Homogenization Analysis in Finite Elasticity: Material and Structural Instabilities on the Micro- and Macro-Scales of Periodic Composites and Their Interaction
,” Comput. Meth. Appl. Mech. Eng.
, 191
(44
), pp. 4971
–5005
. 10.1016/S0045-7825(02)00391-214.
Romanoff
, J.
, and Varsta
, P.
, 2007
, “Bending Response of Web-Core Sandwich Plates
,” Compos. Struct.
, 81
(2
), pp. 292
–302
. 10.1016/j.compstruct.2006.08.02115.
Mindlin
, R. D.
, 1963
, Micro-Structure in Linear Elasticity
, Department of Mechanical Engineering, University of British Columbia, Columbia University
, New York
.16.
Eringen
, A. C.
, 1972
, “Nonlocal Polar Elastic Continua
,” Int. J. Eng. Sci.
, 10
(1
), pp. 1
–16
. 10.1016/0020-7225(72)90070-517.
Reddy
, J. N.
, 2011
, “Microstructure-Dependent Couple Stress Theories of Functionally Graded Beams
,” J. Mech. Phys. Solids
, 59
(11
), pp. 2382
–2399
. 10.1016/j.jmps.2011.06.00818.
Romanoff
, J.
, and Reddy
, J. N.
, 2014
, “Experimental Validation of the Modified Couple Stress Timoshenko Beam Theory for Web-Core Sandwich Panels
,” Compos. Struct.
, 111
(1
), pp. 130
–137
. 10.1016/j.compstruct.2013.11.02919.
Romanoff
, J.
, Reddy
, J. N.
, and Jelovica
, J.
, 2016
, “Using Non-Local Timoshenko Beam Theories for Prediction of Micro- and Macro-Structural Responses
,” Compos. Struct.
, 156
(1
), pp. 410
–420
. 10.1016/j.compstruct.2015.07.01020.
Romanoff
, J.
, Jelovica
, J.
, Avi
, E.
, Reinaldo Goncalves
, B.
, Körgesaar
, M.
, Raikunen
, J.
, Remes
, H.
, Niemelä
, A.
, Reddy
, J. N.
, and Varsta
, P.
, 2016
, “Use of a Equivalent Single Layer Plate Theory in Ship Structural Design
,” Proceedings of PRADS2016
, Copenhagen, Denmark
, Sept. 4–8
, pp. 1
–8
.21.
Remes
, H.
, Romanoff
, J.
, Lillemäe
, I.
, Frank
, D.
, Liinalampi
, S.
, Lehto
, P.
, and Varsta
, P.
, 2017
, “Factors Affecting the Fatigue Strength of Thin-Plates in Large Structures
,” Int. J. Fatigue
, 101
(2
), pp. 397
–407
. 10.1016/j.ijfatigue.2016.11.01922.
Eggert
, L.
, Fricke
, W.
, and Paetzold
, H.
, 2012
, “Fatigue Strength of Thin-Plated Block Joints With Typical Shipbuilding Imperfections
,” Weld. World.
, 56
(11–12
), pp. 119
–128
. 10.1007/BF0332140223.
Lillemäe
, I.
, Liinalampi
, S.
, Remes
, H.
, Itävuo
, A.
, and Niemelä
, A.
, 2017
, “Fatigue Strength of Thin Laser-Hybrid Welded Full-Scale Deck Structure
,” Int. J. Fatigue
, 95
(1
), pp. 282
–292
. 10.1016/j.ijfatigue.2016.11.01224.
Ehlers
, S.
, and Varsta
, P.
, 2009
, “Strain and Stress Relation for Non-Linear Finite Element Simulations
,” Thin Walled Struct.
, 47
(11
), pp. 1203
–1217
. 10.1016/j.tws.2009.04.00525.
Körgesaar
, M.
, and Romanoff
, J.
, 2013
, “Influence of Softening on Fracture Propagation in Large-Scale Shell Structures
,” Int. J. Solids Struct.
, 50
(24
), pp. 3911
–3921
. 10.1016/j.ijsolstr.2013.07.02726.
Hogström
, P.
, and Ringsberg
, J. W.
, 2012
, “An Extensive Study of a Ship's Survivability After Collision—A Parameter Study of Material Characteristics, Non-Linear FEA and Damage Stability Analyses
,” Mar. Struct.
, 27
(1
), pp. 1
–28
. 10.1016/j.marstruc.2012.03.00127.
Ehlers
, S.
, 2010
, “Strain and Stress Relation Until Fracture for Finite Element Simulations of a Thin Circular Plate
,” Thin Walled Struct.
, 48
(1
), pp. 1
–8
. 10.1016/j.tws.2009.08.00428.
Körgesaar
, M.
, Remes
, H.
, and Romanoff
, J.
, 2014
, “Size Dependent Response of Large Shell Elements Under In-Plane Tensile Loading
,” Int. J. Solids Struct.
, 51
(21–22
), pp. 3752
–3761
. 10.1016/j.ijsolstr.2014.07.01229.
Körgesaar
, M.
, Reinaldo Goncalves
, B.
, Romanoff
, J.
, and Remes
, H.
, 2016
, “Behaviour of Orthotropic Web-Core Steel Sandwich Panels Under Multi-Axial Tension
,” Int. J. Mech. Sci.
, 115–116
(1
), pp. 428
–437
. 10.1016/j.ijmecsci.2016.07.02130.
Reinaldo Goncalves
, B.
, Jelovica
, J.
, and Romanoff
, J.
, 2016
, “A Homogenization Method for Geometric Nonlinear Analysis of Sandwich Structures With Initial Imperfections
,” Int. J. Solids Struct.
, 87
(1
), pp. 194
–205
. 10.1016/j.ijsolstr.2016.02.00931.
Metsälä
, M.
, 2016
, “Geometrically Nonlinear Bending Response of Steel Sandwich Box Girder Using Equivalent Single Layer Theory
,” M.Sc. thesis
, Aalto University, School of Engineering,
Espoo
.32.
Dowling
, P. J.
, Chatterjee
, S.
, Frieze
, P.
, and Moolani
, F. M.
, 1973
, “Experimental and Predicted Collapse Behaviour of Rectangular Steel box Girders
,” International Conference on Steel Box Girder Bridges
, London
, Feb. 13–14
, pp. 77
–94
.33.
Gordo
, J. M.
, and Guedes Soares
, C.
, 2004
, “Experimental Evaluation of the Ultimate Bending Moment of a Box Girder
,” Mar. Syst. Offshore Technol.
, 1
(1
), pp. 33
–46
. 10.1007/BF0344919234.
Gordo
, J. M.
, and Guedes Soares
, C.
, 2009
, “Tests on Ultimate Strength of Hull Box Girders Made of High Tensile Steel
,” Mar. Struct.
, 22
(4
), pp. 770
–790
. 10.1016/j.marstruc.2009.07.00235.
Gordo
, J. M.
, and Guedes Soares
, C.
, 2015
, “Experimental Evaluation of the Ultimate Bending Moment of a Slender Thin-Walled Box Girder
,” J. Offshore Mech. Arct. Eng.
, 137
(2
), p. 021604
. 10.1115/1.402953636.
Chakarov
, K.
, Garbatov
, Y.
, and Guedes Soares
, C.
, 2008
, “Fatigue Analysis of Ship Deck Structure Accounting for Imperfections
,” Int. J. Fatigue
, 30
(10–11
), pp. 1881
–1897
. 10.1016/j.ijfatigue.2008.01.01537.
Frank
, D.
, Romanoff
, J.
, and Remes
, H.
, 2013
, “Fatigue Strength Assessment of Laser Stake-Welded Web-Core Steel Sandwich Panels
,” Fatigue Fract. Eng. Mater. Struct.
, 36
(8
), pp. 724
–737
. 10.1111/ffe.1203838.
Fricke
, W.
, and Feltz
, O.
, 2013
, “Factors Between Small-Scale Specimens and Large Components on the Fatigue Strength of Thin-Plated Block Joints in Shipbuilding
,” Fatigue Fract. Eng. Mater. Struct.
, 36
(12
), pp. 1223
–1231
. 10.1111/ffe.1205839.
Fricke
, W.
, Remes
, H.
, Feltz
, O.
, Lillemäe
, I.
, Tchuindjang
, D.
, Reinert
, T.
, Nevierov
, A.
, Sichermann
, W.
, Brinkmann
, M.
, Kontkanen
, T.
, Bohlmann
, B.
, and Molter
, L.
, 2015
, “Fatigue Strength of Laser-Welded Thin-Plate Ship Structures Based on Nominal and Structural Hot-Spot Stress Approach
,” Ships Offshore Struct.
, 10
(1
), pp. 39
–44
. 10.1080/17445302.2013.85020840.
Hashemzadeh
, M.
, Garbatov
, Y.
, and Guedes Soares
, C.
, 2017
, “Analytically Based Equations for Distortion and Residual Stress Estimations of Thin Butt-Welded Plates
,” Eng. Struct.
, 137
(1
), pp. 115
–124
. 10.1016/j.engstruct.2017.01.04141.
Lillemäe-Avi
, I.
, Remes
, H.
, Dong
, Y.
, Garbatov
, Y.
, Quéméner
, Y.
, Eggert
, L.
, Sheng
, Q.
, and Yue
, J.
, 2017
, “Benchmark Study on Considering Welding-Induced Distortion in Structural Stress Analysis of Thin-Plate Structures
,” Proceedings of MARSTRUCT 2017—Progress in the Analysis and Design of Marine Structures
, Lisbon, Portugal
, May 8–10
, CRC Press
, London
, pp. 387
–394
.42.
Lillemäe
, I.
, Lammi
, H.
, Molter
, L.
, and Remes
, H.
, 2012
, “Fatigue Strength of Welded Butt Joints in Thin and Slender Plates
,” Int. J. Fatigue
, 44
(1
), pp. 98
–106
. 10.1016/j.ijfatigue.2012.05.00943.
Roland
, F.
, and Reinert
, T.
, 2000
, “Laser Welded Sandwich Panels for the Shipbuilding Industry
,” Lightweight Construction—Latest Developments
, London
, Feb. 24–25
, SW1
, pp. 1
–12
.44.
Marsico
, T. A.
, Denney
, P.
, and Furio
, A.
, 1993
, “Laser-Welding of Lightweight Structural Steel Panels
,” Proceedings of Laser Materials Processing Conference
, Orlando, FL
, Oct. 24–28
, ICALEO
, pp. 444
–451
.45.
Romanoff
, J.
, Ehlers
, S.
, and Remes
, H.
, 2016
, “Influence of Nonsymmetric Steel Sandwich Panel Joints on Response and Fatigue Strength of Passenger Ship Deck Structures
,” J. Ship. Prod. Des.
, 32
(1
), pp. 1
–9
. 10.5957/JSPD.32.3.15001846.
Fricke
, W.
, 2003
, “Review: Fatigue of Welded Joints: State of Development
,” Mar. Struct.
, 16
(3
), pp. 185
–200
. 10.1016/S0951-8339(02)00075-847.
Byklum
, E.
, and Amdahl
, J.
, 2002
, “A Simplified Method for Elastic Large Deflection Analysis of Plates and Stiffened Panels due to Local Buckling
,” Thin Walled Struct.
, 40
(11
), pp. 925
–953
. 10.1016/S0263-8231(02)00042-348.
Byklum
, E.
, Steen
, E.
, and Amdahl
, J.
, 2004
, “A Semi-Analytical Model for Global Buckling and Postbuckling Analysis of Stiffened Panels
,” Thin Walled Struct.
, 42
(5
), pp. 701
–717
. 10.1016/j.tws.2003.12.00649.
Matouš
, K.
, Geers
, M. G. D.
, Kouznetsova
, V. G.
, and Gillmann
, A.
, 2017
, “A Review of Predictive Nonlinear Theories for Multiscale Modeling of Heterogeneous Materials
,” J. Comput. Phys.
, 330
(1
), pp. 192
–220
. 10.1016/j.jcp.2016.10.07050.
Srinivasa
, A. R.
, and Reddy
, J. N.
, 2017
, “An Overview of Theories of Continuum Mechanics With Nonlocal Elastic Response and a General Framework for Conservative and Dissipative Systems
,” Appl. Mech. Rev.
, 69
(3
), p. 030802
. 10.1115/1.403672351.
Reinaldo Goncalves
, R.
, and Romanoff
, J.
, 2018
, “Size-Dependent Modelling of Elastic Sandwich Beams With Prismatic Cores
,” Solids Struct.
, 136–137
(1
), pp. 28
–37
. 10.1016/j.ijsolstr.2017.12.00152.
Karttunen
, A. T.
, Reddy
, J. N.
, and Romanoff
, J.
, 2018
, “Micropolar Modeling Approach for Periodic Sandwich Beams
,” Compos. Struct.
, 185
(1
), pp. 656
–664
. 10.1016/j.compstruct.2017.11.06453.
Fleck
, N. A.
, and Hutchinson
, J. W.
, 1993
, “A Phenomenological Theory for Strain Gradient Effects in Plasticity
,” J. Mech. Phys. Solids.
, 41
(12
), pp. 1825
–1857
. 10.1016/0022-5096(93)90072-N54.
Fleck
, N. A.
, Muller
, G. M.
, Ashby
, M. F.
, and Hutchinson
, J. W.
, 1994
, “Strain-Gradient Plasticity: Theory and Experiment
,” Acta Metall. Mater.
, 42
(2
), pp. 475
–487
. 10.1016/0956-7151(94)90502-955.
Peerlings
, R. H. J.
, Geers
, M. G. D.
, de Borst
, R.
, and Brekelmans
, W. A. M.
, 2001
, “A Critical Comparison of Non-Local and Gradient-Enhanced Softening Continua
,” Solids Struct.
, 38
(44–45
), pp. 7723
–7746
. 10.1016/S0020-7683(01)00087-756.
Bažant
, Z. P.
, and Jirásek
, M.
, 2002
, “Nonlocal Integral Formulations of Plasticity and Damage: Survey of Progress
,” J. Eng. Mech.
, 128
(11
), pp. 1119
–1149
. 10.1061/(ASCE)0733-9399(2002)128:11(1119)Copyright © 2019 by ASME
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