Timoshenko Kiriş Teorisi Kullanılarak Lamine Kompozit ve Sandviç Kirişlerin Eğilme Analizleri
Timoshenko kiriş teorisi ve Simetrik Düzgünleştirilmiş Parçacık Hidrodinamiği (SDPH) yöntemi kullanılarak çeşitli sınır koşullarına sahip lamine kompozit ve sandviç kirişlerin static davranışları incelenmiştir. Problemin çözümü için Taylor serisi açılımında 6.mertebeye kadar türev ifadelerini içeren SDPH algoritması geliştirilmiştir. Çeşitli sınır koşullarına ve en boy oranlarına sahip simetrik ve simetik olmayan çapraz destekli kompozit kiriş problemleri çözülerek doğrulama ve yakınsaklık çalışmaları gerçekleştirilmiştir. Sunulan yöntemin doğruluğunu sağlamak üzere boyutsuz formda elde edilen orta nokta çökmesi, eksenel ve kayma gerilme değerleri daha önceki çalışmalardan elde edilen sonuçlarla karşılaştırılmıştır. Fiber açısının, lamine yerleşimlerinin, ve en boy oranlarının orta nokta çökmesi ve gerilmeler üzerindeki etkileri çalışılmıştır. Aynı zamanda, karşılaştırma amacıyla hem yakınsaklık hem de detaylı analiz çalışmaları için çözülen problemler Euler-Bernoulli kiriş teorisi kullanılarak da çözülmüştür.
Flexure Analysis of Laminated Composite and Sandwich Beams Using Timoshenko Beam Theory
The static behaviour of laminated composite and sandwich beams subjected to various sets of boundary conditions is investigated by using the Timoshenko beam theory and the Symmetric Smoothed Particle Hydrodynamics (SSPH) method. In order to solve the problem, a SSPH code which consists of up to sixth order derivative terms in Taylor series expansion is developed. The validation and convergence studies are performed by solving symmetric and anti-symmetric cross-ply composite beam problems with various boundary conditions and aspect ratios. The results in terms of mid-span deflections, axial and shear stresses are compared with those from previous studies to validate the accuracy of the present method. The effects of fiber angle, lay-up and aspect ratio on mid-span displacements and stresses are studied. At the same time, the problems not only for the convergence analysis but also for the extensive analysis are also solved by using the Euler-Bernoulli beam theory for comparison purposes.
___
- Nguyen T.K., Nguyen N.D., Vo T.P., Thai H.T.,
“Trigonometric-series solution for analysis of laminated
composite beams”, Compos Struct, 160:142-151, (2017).
- Timoshenko S.P., Goodier J.C., “Theory of Elasticity”,
McGraw-Hill Co. Inc., New York, 1970.
- Wang C.M., Reddy J.N., Lee, K.H., “Shear Deformable
Beams and Plates Relations with Classical Solutions”,
Elsevier Science Ltd., Oxford 2000.
- Kant T., Manjunath B.S., “Refined theories for composite
and sandwich beams with C0 finite elements”, Comput
Struct, 33(3):755–764, (1989).
- Khdeir A.A., Reddy J.N., “An exact solution for the
bending of thin and thick cross-ply laminated beams”,
Compos Struct 37(2):195–203, (1997).
- Soldatos K.P., Watson P., “A general theory for the
accurate stress analysis of homogeneous and laminated
composite beams”, Int J Solids Struct. 34(22): 2857–
2885, (1997).
- Shi G., Lam K.Y., Tay T.E., “On efficient finite element
modeling of composite beams and plates using higher-
order theories and an accurate composite beam element”,
Compos Struct, 41(2):159–165, (1998).
- Zenkour A. M., “Transverse shear and normal
deformation theory for bending analysis of laminated and
sandwich elastic beams”, Mechanics of Composite
Materials & Structures, 6(3): 267-283 (1999).
- Karama M., Afaq K.S., Mistou S., “Mechanical behaviour
of laminated composite beam by the new multi-layered
laminated composite structures model with transverse
shear stress continuity”, Int J Solids Struct., 40(6):1525–
1546, (2003).
- Murthy M.V.V.S., Mahapatra D.R., Badarinarayana K.,
Gopalakrishnan S., “A refined higher order finite element
for asymmetric composite beams”, Compos Struct,
67(1):27–35, (2005).
- Vidal P., Polit O., “A family of sinus finite elements for
the analysis of rectangular laminated beams”, Compos
Struct, 84(1):56–72, (2008).
- Aguiar R.M., Moleiro F., Soares C.M.M., “Assessment
of mixed and displacement-based models for static
analysis of composite beams of different cross-sections”,
Compos Struct, 94 (2):601–616, (2012).
- Nallim L.G., Oller S., Onate E., Flores F.G., “A
hierarchical finite element for composite laminated
beams using a refined zigzag theory”, Compos Struct,
163:168–184, (2017).
- Vo T.P., Thai H.T., Nguyen T.K., Lanc D., Karamanli
A., “Flexural analysis of laminated composite and
sandwich beams using a four-unknown shear and normal
deformation theory”, Compos Struct, 176:388-397,
(2017).
- Donning B.M., Liu W.K., “Meshless methods for shear-
deformable beams and plates”, Computer Methods in
Applied Mechanics and Engineering, 152:47-71, (1998).
- Gu Y.T., Liu G.R., “A local point interpolation method
for static and dynamic analysis of thin beams”, Computer
Methods in Applied Mechanics and Engineering,
190(42):5515-5528, (2001).
- Ferreira A.J.M., Roque C.M.C., Martins P.A.L.S.,
“Radial basis functions and higher-order shear
deformation theories in the analysis of laminated
composite beams and plates” Compos Struct, 66:287-
293, (2004).
- Ferreira A.J.M., Fasshauer G.E., “Computation of natural
frequencies of shear deformable beams and plates by an
RBF-pseudospectral method”, Computer Methods in
Applied Mechanics and Engineering, 196:134-146,
(2006).
- Moosavi M.R., Delfanian F., Khelil A., “The orthogonal
meshless finite volume method for solving Euler–
Bernoulli beam and thin plate problems”, Finite
Elements in Analysis and Design, 49:923-932, (2011).
- Wu C.P., Yang S.W., Wang Y.M., Hu H.T., “A meshless
collocation method for the plane problems of functionally
graded material beams and plates using the DRK
interpolation”, Mechanics Research Communications,
38:471-476, (2011).
- Roque C.M.C., Figaldo D.S., Ferreira A.J.M., Reddy
J.N., “A study of a microstructure-dependent composite
laminated Timoshenko beam using a modified couple
stress theory and a meshless method”, Compos Struct,
96:532-537, (2013).
- Karamanli A., “Elastostatic analysis of two-directional
functionally graded beams using various beam theories
and Symmetric Smoothed Particle Hydrodynamics
method”, Compos Struct, 160:653-669, (2017).
- Karamanli A., “Bending behaviour of two directional
functionally graded sandwich beams by using a quasi-3d
shear deformation theory”, Compos Struct, 160:653-669,
(2017).
- Ferreira A.J.M., Roque C.M.C., Martins P.A.L.S.,
“Radial basis functions and higher order shear
deformation theories in the analysis of laminated
composite beams and plates”, Compos Struct, 66:287-
293, (2004).
- Ferreira A.J.M., “Thick composite beam analysis using a
global meshless approximation based on radial basis
functions”, Mech Adv Mater Struct, 10:271–84, (2003).
- Roque C.M.C., Fidalgo D.S., Ferreira A.J.M., Reddy
J.N., “A study of a microstructure dependent composite
laminated Timoshenko beam using a modified couple
stress theory and a meshless method”, Compos Struct,
96:532-537, (2013).
- Liew K.M., Lim H.K., Tan M.J., He X.Q., “Analysis of
laminated composite beams and plates with piezoelectric
patches using the element-free Galerkin method”,
Computational Mechanics, 29:486-497, (2002).