Abstract
The objective function (Bhatti, Practical optimization methods: with mathematica applications, Springer, New York, 2000 [1]; Brandt et al, Criteria and methods of structural optimization, Martinus Nijhoff Publishers, PWN - Polish Scientific Publishers, Dordrecht, Warszawa, 1986, [2]; Rao, Engineering optimization: theory and practice. Wiley, Hoboken, 2009, [3]) for fitting of the criterion to the measured data can be formulated in many ways, which lead to different results. The following three kinds of objective functions
-
mathematical,
-
physical, and
-
geometrical
can be considered (Altenbach et al, Plasticity of pressure-sensitive materials. Springer, Berlin, pp 49–152, 2014, [4]; Kolupaev et al, Strength hypothesis applied to hard foams Appl Mech Mater, 70, 99–104, 2011, [5]).
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
References
Bhatti MA (2000) Practical optimization methods: with Mathematica applications. Springer, New York
Brandt AM, Dzieniszewski W, Jendo S, Marks W, Owczarek S, Wasiutyński Z (1986) Criteria and methods of structural optimization. Martinus Nijhoff Publishers, PWN - Polish Scientific Publishers, Dordrecht, Warszawa
Rao SS (2009) Engineering optimization: Theory and practice. Wiley, Hoboken
Altenbach H, Bolchoun A, Kolupaev VA (2014) Phenomenological yield and failure criteria. In: Altenbach H, Öchsner A (eds) Plasticity of pressure-sensitive materials. Engineering Materials. Springer, Berlin, pp 49–152
Kolupaev VA, Bolchoun A, Altenbach H (2011) Strength hypothesis applied to hard foams. Appl Mech Mater 70:99–104 Advances in Experimental Mechanics VIII
Bronstein IN, Semendjajew KA (2007) Handbook of mathematics. Springer, Berlin
Fichtenholz GM (1997) Differential- und Integralrechnung, vol 1. Harri Deutsch, Frankfurt am Main
Wu EM (1973) Phenomenological anisotropic failure criterion. In: Broutman LJ, Krock RH, Sendeckyi GP (eds) Treatise on composite materials, vol 2. Academic Press, New York, pp 353–431
Kolupaev VA (2006) 3D-Creep behaviour of parts made of non-reinforced thermoplastics (in German: Dreidimensionales Kriechverhalten von Bauteilen aus unverstärkten Thermoplasten). Dissertation, Martin-Luther-Universität Halle-Wittenberg, Halle-Saale
Kolupaev VA, Kraatz A, Moneke M, Bolchoun A (2006) Description of the multiaxial creep for hard foams (in German: Beschreibung der mehraxialen Kriechphänomene bei Hartschaumstoffen). Kautschuk, Gummi, Kunststoffe KGK 59(1–2):17–27
Chong EKP, Zak SH (2008) An introduction to optimization. Wiley, Hoboken
Eschenauer H, Olhoff N, Schnell W (1997) Applied structural mechanics: Fundamentals of elasticity, load-bearing structures, structural optimization. Springer, Berlin
Papageorgiou M (1996) Optimierung: Statische, dynamische, stochastische Verfahren für die Anwendung. Oldenbourg, München
Stadler W (1988) Multicriteria optimization in engineering and the sciences, vol 37. Mathematical concepts and methods in science and engineering. Plenum Press, New York
Kolupaev VA, Yu MH, Altenbach H (2016) Fitting of the strength hypotheses. Acta Mechanica 227(6):1533–1556
Kolupaev VA, Becker W, Massow H, Dierkes D (2014) Design of test specimens from hard foams for the investigation of biaxial tensile strength (in German: Auslegung von Probekörpern aus Hartschaum zur Ermittlung der biaxialen Zugfestigkeit). Forsch Ingenieurwes 78(3–4):69–86
Shaw MC, Sata T (1966) The plastic behavior of cellular materials. Int J Mech Sci 8:469–478
Awaji H, Sato S (1978) A statistical theory for the fracture of brittle solids under multi-axial stresses. Int J Fract 14(1):R13–R16
Huang PC (1986) Fracture criterion of isotropic materials. Technical Report, Naval Surface Warfare Center, DTIC Document, NAVSWC TR 90-76, Dahlgren, Virginia
McAdam DJJ (1946) Fracture of metals under combined stresses. Trans Am Soc Metal 37:538–566
Zhang T (2008) A general constitutive relation for linear elastic foams. Int J Mech Sci 50:1123–1132
Yagn YI (1931) New methods of strength prediction (in Russ.: Novye metody pascheta na prochnost’). Vestnik Inzhenerov i Tekhnikov 6:237–244
DeRuntz JA, Hoffman O (1969) The static strength of syntactic foams. Trans ASME J Appl Mech 36:551–557
Fahlbusch NC (2015) Entwicklung und Analyse mikromechanischer Modelle zur Beschreibung des Effektivverhaltens von geschlossenzelligen Polymerschäumen. Dissertation, Fachbereich Maschinenbau der Technischen, Universität Darmstadt
Fahlbusch NC, Kolupaev VA, Becker W (2016) Generalized limit surfaces – with an example of hard foams. In: Naumenko K, Aßmuss M (eds) Advanced methods of continuum mechanics for materials and structures, vol 60. Advanced Structured Materials. Springer Science + Business Media, Singapore, pp 337–365
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
Copyright information
© 2018 Springer International Publishing AG
About this chapter
Cite this chapter
Kolupaev, V.A. (2018). Fitting of Criteria. In: Equivalent Stress Concept for Limit State Analysis. Advanced Structured Materials, vol 86. Springer, Cham. https://doi.org/10.1007/978-3-319-73049-3_12
Download citation
DOI: https://doi.org/10.1007/978-3-319-73049-3_12
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-319-73048-6
Online ISBN: 978-3-319-73049-3
eBook Packages: EngineeringEngineering (R0)