Nunziante: theory of elastic bending of curved beams

The plates bending are a characteristic issue in hull ship. I suggest the following references:

- S. Y. Hwang, C. H. Ryu, J. H. Lee, Localization between curved shell plates and its unfolded shape in different coordinate systems for ship-hull plate forming, Mathematical Problems in Engineering Vol. 2011, pp 1-15 (2011).

- C. Ryu, K. S. Kim, Advanced and automatic determination of initial configuration of curved shell plates for flame bending, Journal of Materials Processing Technology Vol 203-1-3, pp 232-240 (2008).

- C. Ryu, J. G. Shin, Optimal approximated unfolding of general curved shell paltes based on deformation theory, Journal of Manufacturing Science and Engineering, Vol 128, pp 261-269 (2006).

- J. S. Yoon, C. Ryu, J. H. Lee, Developablepolynomialsurface approximation to smooth surfaces for fabrication parameters of a large curved shell plate by Differential Evolution, Computer-Aided Design, Vol 40-9, pp 905-915 (2008).

- S. Y. Hwang, J. H. Lee, Y. S. Yang, M. J. Yoo, Springback adjustment for multi-point forming of thick plates in shipbuilding, Computer-Aided Design, Vol 42-11, pp 1001-1012 (2010).

- Z. Xuebiao, J. Zhuoshang nad L. Yujun, Curvature Analysis for Ship-Hull Plate Forming. Journal of Ship Production, Vol. 21 pp. 65-72 (2005)

thank you Gianpaolo.I will search for these lits

For an initial study, the Masters thesis " A study of large deflection of beams and plates" by V.N.Vinesh 2011 available for download and the reference cited in would serve the purpose. The following papers by D.Bushnell would be of much use or further research.

1.A strategy for the solution of problems involving large deflections, plasticity and

creep in IJNM 1977

2. Bifurcation buckling of shells of revolution including large deflections, plasticity

and creep in IJSS 1974

3. B0S0R5—program for buckling of elastic-plastic complex shells of revolution

including large deflections and creep

Computers and structures , 1976

Study on plate bending with large deflections was made by Breslavsky(2012)in journal Sound & Vibration

Chinh

Thanks Chinh,can you pls be more specific..I couldn't get it!!!

The basic well-known theory of Eulero-Bernulli for bending of beams, or that by Timoshenko, taking into account also shear strain, are present in quite all books of structural mechanics for Engineers.

I am adding in attachment a part of my book edited in italian language by McGraw-Hill for italian students, which could be useful as initial reading.

Please, if necessary, do not hesitate to contact me for more questions.

L.Nunziante.

e-mail: [email protected]

Thank you sir, for your reply.

I am little uneasy with a problem like this:

Consider two situations:A.Suppose I have a beam which is always linear elastic and initially straight and I assume that the plane section before and after bending will remain plane. If the applied moment is large enough then this will undergo large deflections which will lead to considerable curvature .Since the plane section remains plane after bending is assumed, the strains will be linear along the depth which implies stress also to be linear along the depth.

B.Instead of straight beam if I had considered a curved beam formulation (to start with a very small curvature) then my end stress profile would have been non linear.(keeping every other things same as in A)

Can you please help me understand this problem !!

Dear Pandit,

attached to this message please you will find the outline of my book of structural mechanics and the pages containing theory and applications necessary to understand the bending of elastic curved beams. This joined to the theory of stright beams given Yesterday, could help you to understand the problem.

Please, let me know if this support will result useful for you.

Best regards,

Luciano Nunziante.

Nunziante: theory of elastic bending of curved beams

Theory of elastic bending of straight beams

Thank you sir

The attachments are really good and useful!!

May be it will be interesting for you: "Relaxation and Creep in Twist and Flexure",

Multidiscipline Modeling in Materials and Structures, accepted, to be published recently.

Abstract:

Multidiscipline Modeling in Materials and Structures

Thank you; it will be useful if you would attach to your message the basic procedure of your treatment, before to obtain the whole paper, if of interest.

Best regards,

L.Nunziante.

I've just submitted a raw text to [email protected].

ABSTRACT:

The aim of the paper is to derive the exact analytical expressions for torsion and bending creep of rods with the Norton-Bailey, Garofalo and Naumenko-Altenbach-Gorash constitutive models. These simple constitutive models, for example, the time- and strain-hardening constitutive equations, were based on adaptations for time-varying stress of equally simple models for the secondary creep stage from constant load/stress uniaxial tests where minimum creep rate is constant. The analytical solution is studied for Norton-Bailey and Garofalo laws in uni-axial states of stress. The most common secondary creep constitutive model has been the Norton-Bailey Law which gives a power law relationship between minimum creep rate and (constant) stress. The distinctive mathematical properties of the power law allowed the development of analytical methods, many of which can be found in high temperature design codes. The results of creep simulation are applied to practically important problem of engineering, namely for simulation of creep and relaxation of helical and disk springs. The exact analytical expressions giving the torque and bending moment as a function of the time were derived.

Thank you for the links !!

Pandit D. .... Please check my publications .. you will find many in beam bending...

Regards...