Analytical solution for bending and buckling response of laminated non-homogeneous plates using a simplified-higher order theory

In this study, analytical solutions for the bending and buckling analysis of simply supported laminated non-homogeneous composite plates based on first and simplified-higher order theory are presented. The simplified-higher order theory assumes that the in-plane rotation tensor is constant through the thickness. The constitutive equations of these theories were obtained by using principle of virtual work. Numerical results for the bending response and critical buckling loads of cross-ply laminates are presented. The effect of non-homogeneity, lamination schemes, aspect ratio, side-to-thickness ratio and in-plane orthotropy ratio on the bending and buckling response were analysed. The obtained results are compared with available elasticity and higher order solutions in the literature. The comparison studies show that simplified-higher order theory can achieve the same accuracy of the existing higher order theory for non-homogeneous thin plate

A computational model of peridynamic theory for deflecting behavior of crack propagation with micro-cracks

The critical effect of micro level defects should be examined at macro level to better understand the fracture behaviors of engineering materials. This study investigates the branching and deflecting behavior of a macro (main) crack in presence of multiple number of micro-cracks at the vicinity of the crack tip. For this purpose, a non-local continuum theory, known as Peridynamics (PD), is utilized based on the original set of bond-based PD equations. The main advantage of using PD is its characteristic superiorities on the modelling of dynamical fracture. Various example problems with inclined-linear and/or curvilinear micro-crack clusters are solved through the implementation of different numerical models to better understand the micro-crack toughening mechanisms. After validating the PD implementation with a benchmark case, several combinations of multiple micro-cracks with various locations are considered. To capture complex forms of crack branches, the positions of micro-cracks are designated to follow an encircling and spreading patterns at the vicinity of the main-crack tip. Hence, more internal energy is dissipated through the generation of new crack surfaces such that the main-crack deflects along a more twisting path. It has been observed that depending on the amount of dissipated energy, the propagation speed of main-crack alters. Also, it has been demonstrated that encircling potential crack propagation regions with micro-cracks provides an augmented toughness to the brittle materials. Overall, the efficiency and robustness of the PD theory are revealed for simulating crack propagation in brittle materials

Dynamic analysis of heterogeneous anisotropic plates resting on the pasternak elastic foundation

Bu makalede, elastik zeminin heterojen ortotropik plakların (HTOP) titreşim frekansları üzerindeki etkileri kayma deformasyon teorisi (KDT) kullanılarak incelenmektedir. İki parametreli elastik ortamın plak üzerindeki reaksiyonunu tanımlamak için Pasternak elastik zemin (PEZ) modeli kullanılmaktadır. Problemin formülasyonu Donnell tipi teoriye dayanır. Heterojen ortotropik malzemenin Young modüllerinin üstel fonksiyon olarak değiştiği, Poisson oranı ve yoğunluğu sabit kabul edilmektedir. Temel denklemler, Galerkin yöntemi kullanılarak zamana bağlı geometrik kısmi türevli diferansiyel denklemler adi diferansiyel denklemlere indirgenmektedir. Türetilen denklemden heterojen ortotropik plakların frekansı için kapalı çözüm elde edilmektedir. Elde edilen değerler literatürdeki benzer çalışmalar ile karşılaştırılarak sonuçlar doğrulanmıştır. Son olarak, heterojenliğin, kayma gerilmelerinin ve PEZ’in frekans parametrelerine etkilerini göstermek için parametrik çalışma gerçekleştirilmiştir.In this study, the effects of elastic foundation on the frequencies of the heterogeneous orthotropic plates using shear deformation plate theory are investigated. Pasternak elastic foundation model is used to define the reaction of two-parameter elastic media on the plate. The formulation of the problem is based on the Donnell type plate theory. The Young's moduli of heterogeneous orthotropic material change as exponential function, Poisson's ratio and density are considered constant. The basic partial differential equations are reduced to ordinary differential equations using Galerkin method and closed-form solution is obtained for the frequency of heterogeneous orthotropic plates. The obtained values are compared with those in the current literature and the results were confirmed. Finally, a parametric study is performed to show the effects of heterogeneity, shear stresses and elastic foundations on the frequency parameters

Dynamic stability of a non homogeneous orthotropic elastic cylindrical shell under a time dependent external pressure

Bu makalede homojen olmayan ortotrop elastik silindirik bir kabuğun, zamanın bir kuvvet fonksiyonu ile değişen bir dış basınç etkisi altında dinamik stabilitesi incelenmektedir. Önce, homojen olmayan ortotrop elastik silindirik bir kabuğun bir dış basınç altında dinamik stabilite denklemleri çıkarılmaktadır. Daha sonra, Saçenkov metodu [1] uygulanarak kritik yük ve dinamiklik katsayısı için genel formüller elde edilmektedir. Son olarak da, bazı özel durumlar için hesaplar yapılıp malzemenin homojen olmayışından dolayı kritik yük ve dinamiklik katsayısına gelen etkiler incelenmektedir.The paper considers the dynamic stability of a non-homogeneous orthotropic elastic cylindrical shell under the effect of an external pressure varying with a power function of time. At first, the dynamic stability equations of a non-homogeneous orthotropic elastic cylindrical shell are derived. Then, the general formulas for the critical load and the dynamic factor are obtained by applying SaÇenkov's method [1]. Finally, carrying out the computations for some special cases, the effect of the non-homogeneity on the critical load and the dynamic factor are studied

Peridynamic modeling of toughening enhancement in unidirectional fiber-reinforced composites with micro-cracks

The matrix component of composite structures is generally brittle. In any damage occurrence, fracture propagates rapidly through the structure. This study proposes a novel toughening enhancement model for unidirectional (UD) composites to overcome these damage-propagation issues. The toughening mechanism is established by introducing the so-called micro defects/cracks for increasing the toughness of the matrix constituent of the composite structure. Mechanical simulations are performed utilizing a non-local continuum formulation known as Peridynamics (PD). The PD formulation facilitates modeling material discontinuities such as complex crack/defect formations with arbitrary size, orientation, and location features in composite structures. Here, the toughening enhancement models are established by allocating various micro-crack formations in three different fiber orientations (0°, 45°, 90°) of UD composite plates. The toughening effects of micro-crack clusters are thoroughly analyzed by making comprehensive comparisons of the propagation speed of an initially introduced macro-crack and its tip strain energy density. As a result, various micro-crack distributions are established to provide an augmented toughness to the brittle composite materials, and their key features are assessed in detail

Buckling of an orthotropic cylindrical thin shell with continuously varying thickness under a dynamic loading

365-370The buckling of an orthotropic composite cylindrical shell with variable thickness, subjected to a dynamic loading, is reported here. At first, the fundamental relations and Donnell type dynamic buckling equation of an orthotropic cylindrical shell with variable thickness have been obtained. Then, employing Galerkin's method, these equations have been reduced to a time dependent differential equation with variable coefficients. Finally, for different initial conditions and approximation functions, applying the Ritz type variational method, analytical expression has been found for the dynamic factor. Using these results, the effect of the variations of the power of time in the external pressure expression, the loading parameter and the ratios of the Young's moduli on the dynamic factor are studied numerically for the case when the thickness of the cylindrical shell varies as a power and exponential functions. It has been observed that these effects change the dynamic factor of the problem in the heading appreciably