Papers by Keyword: Finite Strip Method

Abstract: The dynamic instability of cylindrical shell panels having longitudinal stiffener is studied by using the developed finite strip method (FSM). The method is formulated using the third order shear deformation shell's theory of Reddy's form and the Koiter-Sanders theory for cylindrical shells is implemented. The lay-up effects of skin as well as the stiffener are investigated.

Abstract: Semi-analytical finite strip method (FSM) for analyzing the buckling behavior of some functionally graded plates is presented in this paper. The plates are assumed to be under three types of mechanical loadings, namely; uniaxial compression, biaxial compression, and biaxial compression and tension. The material properties are assumed to vary in the thickness direction according to the power-law variation in terms of volume fractions of the constituents. Thus, the material properties are estimated from the both Voigt rule of mixtures (VRM) and Mori-Tanaka homogenization method (MTM). Numerical results for a variety of functionally graded plates with different aspect ratio are given and compared.

Abstract: In this paper, the theoretical developments of an exact finite strip for the buckling and initial post-buckling analyses of symmetrically cross-ply laminates are presented. The so-called exact finite strip is developed based on the concept that it is effectively a plate. In the development process, the Von-Karman’s equilibrium equation is solved exactly to obtain the buckling loads and the corresponding form of out-of-plane buckling deflection modes. The investigation of thin flat plate buckling behavior is then extended to an initial post-buckling study with the assumption that the deflected form immediately after the buckling is the same as that obtained for the buckling. The post-buckling study is effectively a single-term analysis, which is attempted by utilizing the so-called semi-energy method. In this method, the Von-Karman’s compatibility equation governing the behavior of symmetrically laminated composite plates is used together with a consideration of the total strain energy of the plate. Through the solution of the compatibility equation, the in-plane displacement functions are developed in terms of the unknown coefficient in the assumed out-of-plane deflection function. These in-plane and out-of-plane deflected functions are then substituted in the total strain energy expressions and the theorem of minimum total potential energy is applied to solve for the unknown coefficient. The developed method is subsequently applied to investigate the relative post-buckling stiffness variations of some representative thin symmetric cross-ply laminates for which the results are also obtained through the application of a semi-analytical finite strip method.

Abstract: In the current study, the critical buckling of functionally graded plates (FGPs) subjected to thermal loads is evaluated using the finite strip method based on the first order shear deformation theory (FSDT). The material properties of these plates are assumed to vary in the thickness direction of the plate according to the power law distribution in terms of volume fractions of the constituents. The plates’ boundary conditions are assumed to be simply supported in all the edges or clamped in side edges and simply supported on the ends. The fundamental eigen-buckling equations for the plates are obtained by discretizing the plate into some strips, called functionally graded strip (FGS). The solution is obtained by the minimization of the total potential energy as well as solving the eigenvalue problem. The effects of material gradient index, aspect ratio and different thermal loadings (i.e. uniform temperature rise and nonlinear temperature change across the thickness) on the critical buckling temperature difference will be presented in some graphical forms.

Abstract: A Reddy type, third order shear deformation theory of shells is applied to the development of two versions of finite strip method (FSM), namely semi-analytical and spline methods, to predict the parametric stability and instability regions in the case of cylindrical moderately thick composite laminated panels. The structures are assumed to be under harmonic in-plane loads in the context of the so-called parametric loading. The linear strain terms are expressed in terms of the Koiter-Sanders theory of shallow shells. In order to demonstrate the capabilities of the developed methods in predicting parametric behavior of the subject structures, some representative results are obtained and compared with those in the literature wherever available.

Abstract: In this paper, the application of previously the semi energy finite strip method (FSM) for the non-linear post-buckling analysis of rectangular anti-symmetric laminates is extended to include the effects of normal pressure loading in addition to the progressive end-shortening. One of the main advantages of the semi-energy FSM is that it is based on the closed form solution of von Kármán’s compatibility equation. The developed finite strip method is applied to analyze the large deflection behavior of anti-symmetric angle ply composite laminated plates with simply supported boundary conditions at its loaded ends. To validate the results, they are compared with those obtained from finite element method (FEM) of analysis.

Abstract: In the current paper, a new semi-energy finite strip method is developed based on the concept of first order shear deformation theory (FSDT) in order to attempt the post-buckling solution for relatively thick composite plates subjected to uniform end-shortening. The main advantage of the semi-energy finite strip method (FSM) is that it is based on the closed form solution of von Karman’s compatibility equation in order to derive the analytical shape functions for the in-plane displacements fields. The developed finite strip method is applied to analyze the post buckling behavior of a relatively thick anti-symmetric cross-ply composite plate with clamped out-of-plane boundary conditions at its loaded ends. The results are discussed in detail and compared with those obtained from finite element method (FEM) of analysis. The study of the results has provided confidence in the validity and capability of the developed finite strip in handling post-buckling problem of relatively thick laminated plates.

Abstract: This paper presents the theoretical developments of an exact finite strip for the buckling and initial post-buckling analyses of symmetrically laminated composite plates. The so-called exact finite strip is developed based on the concept that it is effectively a plate. The present method, which is designated by the name Full-analytical Finite Strip Method in this paper, provides an efficient and extremely accurate buckling solution. In the development process, the Von-Karman’s equilibrium equation is solved exactly to obtain the buckling loads and the corresponding form of out-of-plane buckling deflection modes. The investigation of thin flat plate buckling behavior is then extended to an initial post-buckling study with the assumption that the deflected form immediately after the buckling is the same as that obtained for the buckling. The post-buckling study is effectively a single-term analysis, which is attempted by utilizing the so-called semi-energy method. In this method, the Von-Karman’s compatibility equation governing the behavior of symmetrically laminated composite plates is used together with a consideration of the total strain energy of the plate. Through the solution of the compatibility equation, the in-plane displacement functions are developed in terms of the unknown coefficient in the assumed out-of-plane deflection function. These in-plane and out-of-plane deflected functions are then substituted in the total strain energy expressions and the theorem of minimum total potential energy is applied to solve for the unknown coefficient. The developed method is subsequently applied to analyze the initial post-buckling behavior of some representative thin flat plates for which the results are also obtained through the application of a semi-analytical finite strip method. Through the comparison of the results and the appropriate discussion, the knowledge of the level of capability of the developed method is significantly promoted.