Nonlinear Static Buckling Research Articles

Static buckling analysis and geometrical optimization of magneto-electro-elastic sandwich plate with auxetic honeycomb core

The nonlinear static buckling analysis of magneto-electro-elastic sandwich plate on Pasternak-type elastic foundations subjected to the mechanical, thermal, electric and magnetic loadings is presented in this paper. The sandwich plate is composed of an auxetic honeycomb core with negative Poisson’s ratio and two face sheets made of magneto-electro-elastic​ material. The system basic equations are derived based on the Reddy’s higher order shear deformation plate theory taking into account the effect of von Kármán the kinematic nonlinearity and initial imperfection. The form of possible solutions and electric, magnetic potentials are chosen as trigonometric functions based on two cases of boundary conditions. The relationship between axial compressive loading and dimensionless deflection amplitude is determined by using the Galerkin method. For optimization problem, the Bees algorithm is applied to obtain the maximum value of critical buckling load of the sandwich plate which depends on five geometrical and material parameters. The effects of elastic foundations, temperature increment, geometrical parameters and electric and magnetic potentials on the stability characteristics are investigated in numerical results. The accuracy and reliability of present approach is confirmed by comparisons with the existing results in the literature.

Buckling Properties of a Subsea Function Chamber for Oil/Gas Processing in Deep Waters

Due to the complexity of installations and connections of subsea production equipment and the massive structures involved in a challenging environment, the failure of subsea production equipment could induce enormous loss to the safety and reliability of structures in addition to the cost of the oilfield development. One of the challenges that the subsea production structures face, as it moves to ultra-deep water and polar underwater equipment, is to design subsea shell structures capable of withstanding high external pressures. Hence, a subsea function chamber (SFC) has been lately proposed as a viable solution, which has a high level of safety and reliability, and a technique for the subsea production system. This paper presents a general and efficient buckling and collapse analysis strategy. In this work, the SFC is composed of cylindrical and hemispherical shaped steel material. Initial imperfection-based nonlinear buckling analysis has been carried out to investigate the buckling and risks associated with different thicknesses of the structure. Linear and nonlinear static buckling analyses have been carried out using ABAQUS software. By introducing the nonlinear properties of materials, the nonlinear numerical model of SFC is established. The effects of the thickness of different models and the number of stiffeners on the buckling modes are discussed. The wall thickness is calculated by the Donnell equation and Timoshenko’s classical method. It has been found that the classical solutions given by the Donnell and Timoshenko equations are more accurate for structures with larger lengths and diam. The thickness and number of stiffeners have a great influence on the ultimate buckling external pressure load of SFC structure

Nonlinear Static and Dynamic Buckling Analyses of Imperfect FGP Cylindrical Shells Resting on Nonlinear Elastic Foundation Under Axial Compression

In this paper, semi-analytical and analytical methods for the nonlinear static and dynamic buckling analyses of imperfect functionally graded porous (FGP) cylindrical shells subjected to axial compression are presented. The structure is embedded within a generalized nonlinear elastic foundation, treated as a two-parameter Winkler–Pasternak foundation augmented by a nonlinear cubic stiffness. The material property of the shell changes continuously through the thickness. Two types of FGP distributions, i.e. uniform porosity distribution (UPD) and nonuniform porosity distribution (NPD), are considered. By applying the Galerkin’s method to the von Kármán equations, the buckling of the shells was solved. The fourth-order Runge–Kutta method is utilized to obtain the responses of nonlinear dynamic buckling (NDB). The results obtained for some special cases are compared with those available elsewhere. The effects of various geometrical properties, material parameters and elastic foundation coefficients are investigated on the nonlinear static buckling (NSB) and dynamic buckling (DB) analyses of the shells. It was shown that various types of porosity, imperfection and the elastic foundation parameters have a strong effect on the buckling behaviors of the FGP cylindrical shells.

The Effects of Ply Orientation on Nonlinear Buckling of Aircraft composite Stiffened Panel

In this paper, gradual demand for curved, stiffened panels composite emerged from carbon fiber reinforced plastics (CFRP); these are structures that are frequently used in aerospace engineering. Up to 50% of the primary structure of the Boeing 787 is made up of woven graphite–epoxy. This research emphasizes the buckling analysis of stiffened composite panels using the nonlinear, finite element modeling. The stiffened panel is assumed to be subjected to a uniform axial compression load of . For the nonlinear buckling analysis, a stiffened composite panel is made of carbon fibre composite (CFC) in epoxy, Kevlar in epoxy and E-glass (EG) in epoxy. Due to the fact that there are numerous stiffened composite panels materials, this paper, therefore uses a numerical approach, to present the study and results of the nonlinear static buckling analysis of I-stiffened, on different composite panels. This research also presented the effect of the different ply orientations using Abaqus finite element analysis (FEA).

A new approach for nonlinear buckling analysis of imperfect functionally graded carbon nanotube-reinforced composite plates

This paper presents an analytical approach to analyze the nonlinear static buckling of imperfect functionally graded carbon nano-reinforced composite (FG-CNTRC) plates subjected to axial compression. The material properties of the FG-CNTRC are assumed to be graded through the thickness direction according to several linear distributions of the volume fraction of carbon nanotubes. The theoretical formulations are based on the classical plate theory (Kirchhoff plate) with von Karman-type of nonlinearity and the initial geometrical imperfection. The approximate solution is developed for simply supported and freely movable boundary conditions. By applying the traditional Galerkin method and the Airy stress function, the results for the critical load are obtained in closed-form solutions, which are convenient to be used in engineering design. Some illustrative examples are also presented in details to investigate the effects of the imperfection, carbon nanotubes, and geometrical parameters on the nonlinear static behavior the plates.

Post-buckling of cylindrical shells with spiral stiffeners under elastic foundation

In this paper, an analytical method for the Post-buckling response of cylindrical shells with spiral stiffeners surrounded by an elastic medium subjected to external pressure is presented. The proposed model is based on two parameters elastic foundation Winkler and Pasternak. The material properties of the shell and stiffeners are assumed to be continuously graded in the thickness direction. According to the Von Karman nonlinear equations and the classical plate theory of shells, strain-displacement relations are obtained. The smeared stiffeners technique and Galerkin method is used to solve the nonlinear problem. To valid the formulations, comparisons are made with the available solutions for nonlinear static buckling of stiffened homogeneous and un-stiffened FGM cylindrical shells. The obtained results show the elastic foundation Winkler on the response of buckling is more effective than the elastic foundation Pasternak. Also the ceramic shells buckling strength higher than the metal shells and minimum critical buckling load is occurred, when both of the stiffeners have angle of thirty degrees.

Nonlinear response of imperfect eccentrically stiffened ceramic–metal–ceramic FGM thin circular cylindrical shells surrounded on elastic foundations and subjected to axial compression

In this paper, an analytical approach is presented to investigate the nonlinear static buckling and post-buckling for imperfect eccentrically stiffened functionally graded thin circular cylindrical shells surrounded on elastic foundation with ceramic–metal–ceramic layers (S-FGM) and subjected to axial compression. The Lekhnitsky smeared stiffeners technique with Pasternak type elastic foundation, stress function and Bubnov-Galerkin method are applied. Numerical results are given for evaluating effects of material and geometrical properties, elastic foundations and eccentrically outside stiffeners on the buckling and post-buckling of the S-FGM shells. The obtained results are validated by comparing with those in the literature.

Residual ultimate compressive strength of dented square plates

Thin steel plates are widely used in many structural applications because of its high load carrying capacity with less weight. The load carrying capacity of thin plates mainly depends on its buckling behavior which in turn is affected by the imperfections present in it. Dent is one of the common geometrical imperfections present in thin shell structures which may be formed due to mechanical damage caused by accidental loading or impact. In this work, influence of various dent parameters (dent length, dent width, dent depth and angle of orientation of the dent) on the static ultimate strength of thin square plates of different thicknesses under uniaxial compressive loading is studied. The dent is modeled on the FE surface of perfect thin square plate of size 1000mm (of different thickness) for different sizes and angles of orientation of the dent at the center of the plate. These dented plates are analyzed using non-linear static buckling analysis of general purpose FE software ANSYS V12. From the results obtained, it is found that both shorter and longer dents reduce the ultimate strength drastically. But in case of shorter dents, variation of ultimate strength of dented plates due to variation of size and angle of orientation of dents is insignificant, whereas in the case of longer dents, size and angle of orientation of dents have significant effect. It is also found that the reduction in ultimate strength of thin plates with a dent of same size and orientation increases with increase in shell thickness.

Parametric study on buckling behaviour of dented short carbon steel cylindrical shell subjected to uniform axial compression

Generally, thin cylindrical shells are susceptible for geometrical imperfections like non-circularity, non-cylindricity, dents, swellings, etc. All these geometrical imperfections decrease the static buckling strength of thin cylindrical shells, but in this paper only effect of a dent on strength of a short ( Lc/ Rc∼1, Rc/ t=117, 175, 280) cylindrical shell is considered for analysis. The dent is modeled on the FE surface of perfect cylindrical shell for different angles of inclination and sizes at half the height of cylindrical shell. The cylindrical shells with a dent are analyzed using non-linear static buckling analysis. From the results it is found that in case of shorter dents, size and angle of inclination of dents do not have much effect on static buckling strength of thin cylindrical shells, whereas in the case of long dents, size and angle of inclination of dents have significant effect. But both short and long dents reduce the static buckling strength drastically. It is also found that the reduction in buckling strength of thin cylindrical shell with a dent of same size and orientation increases with increase in shell thickness.

Effect of a Dent of Different Sizes and Angles of Inclination on Buckling Strength of a Short Stainless Steel Cylindrical Shell Subjected to Uniform Axial Compression

Generally, thin cylindrical shells are susceptible for geometrical imperfections like non-circularity, non-cylindricity, dents, swellings etc. All these geometrical imperfections decrease the static buckling strength of thin cylindrical shells, but in this paper only effect of a dent on strength of a short (L / D ∼1 and R/t = 280) stainless steel cylindrical shell is considered for analysis. The dent is modeled on the FE surface of perfect cylindrical shell for different angles of inclination and sizes at half the height of cylindrical shell. The cylindrical shells with a dent are analyzed using non-linear static buckling analysis. From the results it is found that in case of shorter dents, size and angle of inclination dents do not have much effect on static buckling strength of thin cylindrical shells, where as in the case of long dents, size and angle of inclination of dents have significant effect. But both short and long dents reduce the static buckling strength drastically.

A Study on the Static Buckling Load Estimation of the Spacer Grid in the Pressurized Water Reactor Fuel Assembly

This study contains several estimation methods of the static buckling load for the spacer grid of nuclear fuel assembly in pressurized water reactor. Three different estimation methods were proposed for the calculation of the static buckling loads of spacer grid. The linear and non-linear static buckling analyses were performed to estimate the static buckling load of the spacer grids using ANSYS program. The analyses results were compared with the static buckling test results. Based on the analysis and test results, the applicability of the proposed estimation method for the static buckling load of the spacer grid was investigated.