Showing 7 results for Buckling Load
Fatemeh Sohani, Hamidreza Eipakchi,
Volume 13, Issue 14 (3-2014)
Abstract
In this paper, the governing equations for a vibratory beam with moderately large deflection are derived using the first order shear deformation theory. These equations which are a system of nonlinear partial differential equations with constant coefficients are solved analytically with the perturbation technique and the natural frequencies and the buckling load of the system are determined. A parametric study is performed and the effects of the geometrical and material properties on the natural frequency and buckling load are investigated and the effect of normal transverse strain and axial load on natural frequency are examined. Some results based on the first order shear deformation theory are consistent with classic theories of beams and some yield different results. Formulation presented to calculate the transverse frequency, determines the axial frequency too. Also, the natural frequencies and buckling load are calculated with the finite elements method by applying one and three-dimensional elements and the results are compared with the analytical solution.
Reza Zamani, Gholam Hossein Rahimi, Mohammad Hossein Pol, Mohammad Hedayatian,
Volume 15, Issue 3 (5-2015)
Abstract
The current study represents the influence of nanoclay on buckling behavior of glass fiber reinforced polymer (GFRP) grid-stiffened nanocomposite shells. The nanocomposite grid shells were manufactured from continuous glass fiber using a specially designed filament winding machine. The epoxy/clay nanocomposites with different clay content (0%, 1.5%, 3% and 5% of clay) were used as the matrix of the grid stiffened structures. The state of dispersion and mechanical properties of the epoxy/clay nanocomposites were obtained by X-ray diffraction (XRD) method and uniaxial tensile test, respectively and also the grid structures were loaded under uniform axial compression test. The results of XRD show that the clay has been further intercalated by the epoxy matrix. The tensile test results represent that the tensile modulus and Strength, strain to break and energy to break of the epoxy/clay nanocomposites increase with adding clay loading into the epoxy resin. Furthermore, it is found that the critical buckling load of the cylindrical grid samples increases continuously with increasing the clay content up to 5 wt. %. The maximum value of improvement in the critical buckling load is about 10% for the samples with 5 wt. % of nanoclay.
Amir Reza Shahani, Roohollah Mohammadjani,
Volume 15, Issue 6 (8-2015)
Abstract
The instability behavior of stiffened cylindrical shells and determination of the corresponding buckling loads under axial compression, according to the extended range of structural applications of them in various fields of engineering, has been paid a lot of attention from researchers and extensive amount of studies have been performed on it so far. Because of a lack of the general closed form responses due to complexity of the governing equations and analyses process, using the FE software codes as the main technique of the stiffened shell's buckling load determination is inevitable. Accordingly the present paper has been studied the reinforcement effects of ring and stringer and also compared the buckling loads which are evaluated by analysis of the FE numerical modeling in ABAQUS software with instability results that obtained from a general analytical equation derived by other references via applying the simplifying assumptions to the governing equations. Furthermore an attempt has been performed for extraction of the finite element instability load vs. structure reinforcement correspondence that enables the designers to accurately determine the instability load of structure for other values of structure's stiffening volume without performing additional FE analyses which are much more expensive in term of computer time.
Mohsen Hoseini, Mostafa Talebitooti,
Volume 15, Issue 12 (2-2016)
Abstract
The objective of this investigation is to present a semi-analytical method for studying the buckling of the moderately thick composite conical shells under axial compressive load. In order to derive the equilibrium equations of the conical shell, first order shear deformation shell theory is used. The equilibrium equations are derived by applying the principle of minimum potential energy to the energy function that they are in the type of partial differential equations. In the following, the partial differential equations are transformed to algebraic type by using Galerkin and differential quadrature methods and then the standard eigenvalue equation is formed and critical buckling load is calculated. Also, to validate the results obtained in this study, comparisons are made with outcomes of previous literatures and the results of Abaqus finite element software. Analyzing the results, shows the convergence speed and good accuracy of differential quadrature method and desired precision of Galerkin method in calculating the critical buckling load. Finally, the effect of cone angle, fiber orientation, boundary conditions, ratios of thickness to radius and length to radius of the critical buckling load are studied.
Mahnaz Zakeri, Abolfazel Jafari,
Volume 16, Issue 6 (8-2016)
Abstract
Thin sheets stiffened with lattice structures are used widely in many engineering industries. Investigation of stability behavior for the grid structures and determination of the buckling load under compressive loads is an issue that has attracted the attention of many researchers; and extensive studies have been done in this field. In this paper, a new grid called Diacube is introduced and its buckling load is examined. For this aim, first, the buckling behavior of 5 common types of stiffened flat lattice panels containing hexagonal, triangular, square, diamond and kagome grid are investigated under compressive axial load; and the results are compared with Diacube grid. The effect of network density used in each structure on the buckling of these structures will be studied under different boundary conditions. In addition to common grids,. Regarding to the mass difference of samples, specific critical load parameter (the buckling load to mass ratio) is used for comparison between the structures. Using the finite element modeling and numerical analysis, the grid that has the highest buckling load in each boundary condition is determined It is found that if unloaded edges in lattice panels are simply supported, this new Diacube grid will have the highest buckling load among all structures. Finally, validity of the numerical result obtained for two samples of the structures including hexagonal and Diacube grid is evaluated experimentally; and the numerical results are confirmed.
Volume 25, Issue 1 (3-2026)
Abstract
The use of members with non-uniform cross-sections due to the reduction of the number of materials and the weight of the structure is widely used in industrial structures and metal bridges. Buckling is one of the major problems engineers face in the design of axial compression members (columns). For this reason, several researches have been conducted by researchers in the field of column buckling. Most of the previous research is limited to investigating stability and buckling in Non-prismatic elastic columns in the static state. During an earthquake, the structure is subjected to vertical and lateral earthquake loads. To evaluate the dynamic behavior of the structure during an earthquake, the stability and dynamic buckling of the column must be evaluated. The effect of the earthquake's vertical load and the dynamic axial load has an effect on the dynamic stability of the member in the form of the second-order effect of buckling. In this article, the dynamic buckling of a column with a variable section and viscous damper under alternating axial load is investigated in a comprehensive model. The alternating axial load effect is assumed as a cosine function and the viscous damping effect at the end of the member is assumed as a Dirac delta function. The changes in the moment of inertia along the length of the column are considered in three modes: linear, cubic, and fourth-order changes. The constituent differential equation includes column strain energy, second order effect of alternating axial load, inertia per unit length of the column, and damping of a viscous damper. To solve the constitutive equation, first the weak form of the governing differential equation is written. Lagrange interpolation functions are used as the shape function and the Fourier function (proposed by Bolotin) as the dynamic response of the equation. In the next step, the matrices of material hardness, geometric hardness, and mass are extracted. After extracting the above matrices, the eigenvalues (Buckling load factor, natural frequency) of the equation are checked. Muller root finding technique is used by coding in MATLAB software to calculate eigenvalues. For accuracy in calculations, the function of the form of the equation is checked by the Lagrange method with the number of thirty terms. Also, finding the roots of the equation to calculate the eigenvalue is done with a step of 0.05 using Mueller's method. The buckling load coefficient of the column is evaluated for different values of the expansion coefficient and the damping percentage of the viscous damper in different boundary conditions. The results show that the mentioned values have a significant effect on the changes in the buckling load factor in terms of excitation frequency and resonance frequency. Depending on the boundary conditions, increasing the opening factor causes the diagram to move to the right or left side of the dimensionless excitation frequency axis. Also, increasing the damping coefficient of the viscous damper causes the diagram to move to the left side of the dimensionless excitation frequency axis. Dimensionless parameters such as bar coefficient, excitation frequency, and opening coefficient have been used to report the dynamic behavior of the set in all the tables and figures. The results of this research can be generalized for the design of columns under periodic axial load. The results of this article are verified and compared with previous research. There is an acceptable agreement between the results of the present article and previous research.
Volume 25, Issue 2 (7-2025)
Abstract
Beams placed on elastic foundations are widely used in simulating a main portion of mechanical and civil structures. The buckling behavior of these beams, including the load and the shape of the buckling mode, is different from normal beams due to the loads imposed by the elastic foundation that is proportional to the beam deflection. Due to their functional modality, these types of beams are generally subjected to repetitive loads (such as railway tracks) and extreme environmental conditions (such as piles and buried pipelines), making them susceptible to damage such as cracks. The presence of these flaws along the members can lead to premature failure of these structural elements due to buckling in the damaged area. Evaluating the stability of such structures considering structural flaws is essential for ensuring their safety. In this context, this paper presents a new method for calculating the closed-form solution to the buckling of cracked beams on elastic foundations. In the proposed method, a concentrated moment is used to model the crack and apply the slope difference caused by the crack at the damage location. Then, the governing differential equations for pin-ended beams are derived, and by using Fourier expansion and calculating the value of applied moment, a closed-form solution is presented to calculate the buckling of beams on elastic foundations. Using this technique for crack modeling makes it easier to solve beam differential equations and achieve a closed-form solution for calculating beam buckling load. Finally, the effects of different parameters such as the bending stiffness of the beam, length of the beam, crack depth, and stiffness of the bed on the buckling load of the beam can be studied. To verify the proposed solution, the results of solving closed-form equations are compared with the exact solutions of simplified problems and the results from finite element models, which confirms the accuracy of the performed calculations. As the current solutions to the buckling of cracked beams on an elastic foundation are mainly based on numerical or finite element methods, the presented closed-form solution in this study can significantly contribute to enhancing the accuracy and facility of calculations in the design and analysis process for such structures.
