Ludwick Tipi Doğrusal Olmayan Malzemeden Yapılmış Bir Konsol Kirişteki Doğrusal Kabullerin Yer Değiştirmeler Üzerindeki Etkisinin İncelenmesi

Yıl 2014, Cilt: 16 Sayı: 2, 15 - 25, 01.12.2014

İbrahim Eren

Öz

Bu çalışmada Ludwick tipi malzemeden yapılmış bir konsol kirişte, serbest uçtan etkiyen moment etkisiyle meydana gelen büyük yer değiştirmelerin hesabında doğrusal kabullerin etkisi incelenmiştir. Malzeme ve geometrik doğrusallaştırmanın etkileri tablo ve şekillerle açıklanmış, geometrik doğrusallaştırmanın, malzemeyi doğrusal kabul etme durumuna göre yer değiştirmeler üzerindeki saptırma etkisinin daha düşük olduğu gösterilmiştir

Anahtar Kelimeler

Büyük yer değiştirmeler, doğrusal olmayan malzeme, geometrik doğrusal olmama

Determining the effect of linearization over the large deflections on cantilever beams made of nonlinear Ludwick type material

Öz

In this study, Linearization effect is investigated for cantilever beams made of Ludwick type material subjected to a moment at the free end. Material and geometrical linearization effects are explained by using tables and figures. It is seen the geometrical linearization effect is lower than the material linearization effect, over the deflections

Anahtar Kelimeler

Large deflections, geometrical non-linearity, material non-linearity

Kaynakça

• Bisshopp, K. E., Drucker, D.C., Large deflections of cantilever beams, The Quarterly of Applied Mathematics, 3, 272-275, (1945).
• Scott, E. J., Carver, D. R. ve Kan M., On the linear differential equation for beam deflection, Journal of Applied Mechanics, 22, 245-248, (1955).
• Lau, J. H., Large deflections of beams with combined loads, Journal of Engineering Mechanics, 108, 180-185, (1982).
• Rao, B. N., Rao, G. V., On the large deflection of cantilever beams with end rotational load, ZAMM - Journal of Applied Mathematics and Mechanics, 66, 507-509, (1986).
• Baker, G., On the large deflections of non- prismatic cantilevers with a finite depth, Computers & Structures, 46, 365-370, (1993).
• Lee, B. K., Wilson, J.F. ve Oh, S.J., Elastica of cantilevered beams with variable cross sections, International Journal of Non-Linear Mechanics, 28, 579-589, (1993).
• Frisch-Fay, R., Flexible Bars, Butter Worths, London, (1962).
• Fertis, D. G., Nonlinear Mechanics, CRC Pres, New York, (1999).
• Prathap, G., Varadan, T. K., The inelastic large deformation of beams, Journal of Applied Mechanics, 43, 689-690, (1976).
• Varadan, T. L., Joseph, D., Inelastic Finite Deflections of Cantilever Beams, Journal of the Aeronautical Society of India, 39, 39-41, (1987).
• Lewis, G., Monosa, F., Large deflections of cantilever beams of non-linear materials, Computers & Structures, 14, 357-360, (1981).
• Lewis, G., Monosa, F., Large deflections of cantilever beams of non-linear materials of the ludwick type subjected to an end moment, International Journal of Non-Linear Mechanics, 17, 1-6, (1982).
• Lo, C.C., Gupta, S.D., Bending of a nonlinear rectangular beam in large deflection, Journal of Applied Mechanics, 45, 213-215, (1978).
• Lee, K., Large deflections of cantilever beams of non-linear elastic material under a combined loading, International Journal of Non-Linear Mechanics, 37, 439443, (2002).
• Güven, U., Baykara, C. ve Bayer, İ., Large deflections of a cantilever beam of nonlinear bimodulus material subjected to an end moment, The Journal of Reinforced Plastics and Composites, 24, 12,1321-1326, (2005).
• Banerjee, A., Bhattacharya, B. ve Mallik, A.K., Large deflection of cantilever beams with geometric non-linearity: Analytical and numerical approaches, International Journal of Non-Linear Mechanics, 43, 5, 366–376, (2008).
• Solano-Carrillo, E., Semi-exact solutions for large deflections of cantilever beams of non-linear elastic behavior. International Journal of Non-Linear Mechanics, 44, 2, 253–256, (2009).
• Chen, L., An integral approach for large deflection cantilever beams, International Journal of Non-Linear Mechanics, 45, 3, 301–305, (2010).
• Vaz, M.A., Caire,M., On the large deflections of linear viscoelastic beams, International Journal of Non-Linear Mechanics, 45,1, 75–81, (2010).
• Mutyalarao, M., Bharathi, D. ve Nageswara Rao, B., Large deflections of a cantilever beam under an inclined end load, Applied Mathematics and Computation, 217, 7, 3607–3613, (2010).
• Hummer, A., Irschik, H., Large deformation and stability of extencible with unknown length, International Journal of Solids and Structures, 48, 9, 13011310, (2011).
• Batista, M., Large deflections of shear-deformable cantilever beam subject to a tip follower force, International Journal of Mechanical Sciences, 75, 388-395, (2013). [23]. Eren, İ., Kirişlerdeki büyük yer değiştirmeler üzerine bazı yeni çözümler, Doktora Tezi, Yıldız Teknik Üniversitesi, Fen Bilimleri Enstitüsü, İstanbul, (2006).