• Journal of Mechanical Science and Technology
• /
• 제17권11호
• /
• pp.1638-1649
• /
• 2003

A study is made on the characterization of damage tolerance by spherical indentation in hardly coated layer structure with modest elastic modulus mismatch. A hard silicon nitride is prepared for the coating material and silicon nitride with 5wt% of boron nitride composites for underlayer. Hot pressing to eliminate the effect of interface delamination during the fracture makes strong interfacial bonding. The elastic modulus mismatch between the layers is not only large enough to suppress the surface crack initiation from the coating layer but sufficiently small to prevent the initiation of radial crack from the interface. The strength degradation of the layer structure after sphere contact indentation does not significantly occur, while the degradation of silicon nitride-boron nitride composite is critical at a high load and high number of contacts.

• Steel and Composite Structures
• /
• 제33권4호
• /
• pp.509-523
• /
• 2019

In the present work, the buckling analysis of micro sandwich plate with an isotropic/orthotropic cores and piezoelectric/polymeric nanocomposite face sheets is studied. In this research, two cases for core of micro sandwich plate is considered that involve five isotropic Devineycell materials (H30, H45, H60, H100 and H200) and an orthotropic material also two cases for facesheets of micro sandwich plate is illustrated that include piezoelectric layers reinforced by carbon and boron-nitride nanotubes and polymeric matrix reinforced by carbon nanotubes under temperature-dependent and hydro material properties on the elastic foundations. The first order shear deformation theory (FSDT) is adopted to model micro sandwich plate and to apply size dependent effects from modified strain gradient theory. The governing equations are derived using the minimum total potential energy principle and then solved by analytical method. Also, the effects of different parameters such as size dependent, side ratio, volume fraction, various material properties for cores and facesheets and temperature and humidity changes on the dimensionless critical buckling load are investigated. It is shown from the results that the dimensionless critical buckling load for boron nitride nanotube is lower than that of for carbon nanotube. It is illustrated that the dimensionless critical buckling load for Devineycell H200 is highest and lowest for H30. Also, the obtained results for micro sandwich plate with piezoelectric facesheets reinforced by carbon nanotubes (case b) is higher than other states (cases a and c).The results of this research can be used in aircraft, automotive, shipbuilding industries and biomedicine.

• Structural Engineering and Mechanics
• /
• 제13권5호
• /
• pp.543-556
• /
• 2002

A dynamic elastic local buckling analysis is presented for a pile subjected to an axial impact load. The pile is assumed to be geometrically perfect. The interactions between the pile and the surrounding soil are taken into account. The interactions include the normal pressure and skin friction on the surface of the pile due to the resistance of the soil. The analysis also includes the influence of the propagation of stress waves through the length of the pile to the distance at which buckling is initiated and the mass of the pile. A perturbation technique is used to determine the critical buckling length and the associated critical time. As a special case, the explicit expression for the buckling length of a pile is obtained without considering soil resistance and compared with the one obtained for a column by means of an alternative method. Numerical results obtained show good agreement with the experimental results. The effects of the normal pressure and the skin friction due to the surrounding soil, self-weight, stiffness and geometric dimension of the cross section on the critical buckling length are discussed. The sudden change of buckling modes is further considered to show the 'snap-through' phenomenon occurring as a result of stress wave propagation.

• Journal of applied mathematics & informatics
• /
• 제27권3_4호
• /
• pp.501-515
• /
• 2009

A second order nonlinear ordinary differential equation is obtained by solving the initial-boundary value problem of a class of elas-todynamics equations, which models the radially symmetric motion of a incompressible hyper-elastic solid sphere under a suddenly applied surface tensile load. Some new conclusions are presented. All existence conditions of nonzero solutions of the ordinary differential equation, which describes cavity formation and motion in the interior of the sphere, are presented. It is proved that the differential equation has singular periodic solutions only when the surface tensile load exceeds a critical value, in this case, a cavity would form in the interior of the sphere and the motion of the cavity with time would present a class of singular periodic oscillations, otherwise, the sphere remains a solid one. To better understand the results obtained in this paper, the modified Varga material is considered simultaneously as an example, and numerical simulations are given.

• Design & Manufacturing
• /
• 제17권4호
• /
• pp.33-41
• /
• 2023

Excessive use of plastic bottles contributes to a significant environmental issue due to the high volume of plastic waste generated. To address this, efforts are needed to reduce the weight of plastic bottles. However, indiscriminate weight reduction may compromise the essential rigidity required for plastic bottles. Extensive research on rib shape for pressure vessels are exists, but there is a few research of rib shapes to enhance the stiffness of plastic bottles. The following results were obtained from the analyses conducted in this study. 1) Among the rib cross-sections of square, trapezoid, and triangle, the buckling critical load of PET bottles with square-shaped ribs is improved by about 14% compared to the buckling critical load of PET bottles without ribs. 2) The buckling critical load is improved by about 18% when a square-shaped rib with an aspect ratio of 0.2 is applied, compared to the buckling critical load of the bottle without the rib. 3) When longitudinal and transverse square ribs were applied to the axial direction of the PET bottle, the buckling critical load was improved by about 32% and 58% compared to the buckling critical load of the PET bottle without ribs, respectively, indicating that applying longitudinal ribs is effective in reinforcing the stiffness of PET bottles. 4) When 14 transverse ribs were applied, the maximum improvement was about 48% compared to the buckling critical load of the plastic bottle without ribs. 5) When 3 longitudinal ribs were applied on each side, the maximum improvement was about 76% compared to the buckling critical load of the bottle without ribs. Therefore, it was concluded that for effective stiffness reinforcement of a 500ml square bottle with a thickness of 0.5mm, 3 square-shaped ribs with an aspect ratio of 0.2 should be applied in the longitudinal direction relative to the axial direction of the bottle.

• Structural Engineering and Mechanics
• /
• 제55권1호
• /
• pp.47-64
• /
• 2015

This paper presents the effect of hybridization material on variation of critical buckling load with different cross-ply laminates plate resting on elastic foundations of Winkler and Pasternak types subjected to combine uniaxial and biaxial loading by using two variable refined plate theories. Governing equations are derived from the principle of virtual displacement; the formulation is based on a new trigonometric shape function of displacement taking into account transverse shear deformation effects vary parabolically across the thickness satisfying shear stress free surface conditions. These equations are solved analytically using the Navier solution of a simply supported. The influence of the various parameters geometric and material, the thickness ratio, and the number of layers symmetric and antisymmetric hybrid laminates material has been investigated to find the critical buckling loads. The numerical results obtained through the present study with several examples are presented to verify and compared with other models with the ones available in the literature.

• Advances in nano research
• /
• 제8권1호
• /
• pp.59-68
• /
• 2020

In the present study, buckling analysis of sandwich composite (carbon nanotube reinforced composite and fiber reinforced composite) Euler-Bernoulli beam in two configurations (core and layers material), three laminates (combination of different angles) and two models (relative thickness of core according to peripheral layers) using differential quadrature method (DQM) is studied. Also, the effects of porosity coefficient and different types of porosity distribution on critical buckling load are discussed. Using sandwich beam, it shows a considerable enhancement in the critical buckling load when compared to ordinary composite. Actually, resistance against buckling in sandwich beam is between two to four times more. It is also showed the critical buckling loads of laminate 1 and 3 are significantly larger than the results of laminate 2. When Configuration 2 is used, the critical buckling load rises about 3 percent in laminate 1 and 3 compared to the results of configuration 1. The amount of enhancement for laminate 3 is about 17 percent. It is also demonstrated that the influence of the core height (thickness) in the case of lower carbon volume fractions is ignorable. Even though, when volume fraction of fiber increases, differences grow smoothly. It should be noticed the amount of decline has inverse relationship with the beam aspect ratio. Among three porosity patterns investigated, beam with the distribution of porosity Type 2 (downward parabolic) has the maximum critical buckling load. At the end, the first three modes of buckling will be demonstrated to investigate the effect of spring constants.

• Advances in aircraft and spacecraft science
• /
• 제4권5호
• /
• pp.585-611
• /
• 2017

This article covenants with the post buckling witticism of carbon nanotube reinforced composite (CNTRC) beam supported with an elastic foundation in thermal atmospheres with arbitrary assumed random system properties. The arbitrary assumed random system properties are be modeled as uncorrelated Gaussian random input variables. Unvaryingly distributed (UD) and functionally graded (FG) distributions of the carbon nanotube are deliberated. The material belongings of CNTRC beam are presumed to be graded in the beam depth way and appraised through a micromechanical exemplary. The basic equations of a CNTRC beam are imitative constructed on a higher order shear deformation beam (HSDT) theory with von-Karman type nonlinearity. The beam is supported by two parameters Pasternak elastic foundation with Winkler cubic nonlinearity. The thermal dominance is involved in the material properties of CNTRC beam is foreseen to be temperature dependent (TD). The first and second order perturbation method (SOPT) and Monte Carlo sampling (MCS) by way of CO nonlinear finite element method (FEM) through direct iterative way are offered to observe the mean, coefficient of variation (COV) and probability distribution function (PDF) of critical post buckling load. Archetypal outcomes are presented for the volume fraction of CNTRC, slenderness ratios, boundary conditions, underpinning parameters, amplitude ratios, temperature reliant and sovereign random material properties with arbitrary system properties. The present defined tactic is corroborated with the results available in the literature and by employing MCS.

• Structural Engineering and Mechanics
• /
• 제25권4호
• /
• pp.383-403
• /
• 2007

The contact problem for an elastic layer resting on an elastic half plane is considered according to the theory of elasticity with integral transformation technique. External loads P and Q are transmitted to the layer by means of two dissimilar rigid flat punches. Widths of punches are different and the thickness of the layer is h. All surfaces are frictionless and it is assumed that the layer is subjected to uniform vertical body force due to effect of gravity. The contact along the interface between elastic layer and half plane will be continuous, if the value of load factor, ${\lambda}$, is less than a critical value, ${\lambda}_{cr}$. However, if tensile tractions are not allowed on the interface, for ${\lambda}$ > ${\lambda}_{cr}$ the layer separates from the interface along a certain finite region. First the continuous contact problem is reduced to singular integral equations and solved numerically using appropriate Gauss-Chebyshev integration formulas. Initial separation loads, ${\lambda}_{cr}$, initial separation points, $x_{cr}$, are determined. Also the required distance between the punches to avoid any separation between the punches and the layer is studied and the limit distance between punches that ends interaction of punches, is investigated. Then discontinuous contact problem is formulated in terms of singular integral equations. The numerical results for initial and end points of the separation region, displacements of the region and the contact stress distribution along the interface between elastic layer and half plane is determined for various dimensionless quantities.

• Steel and Composite Structures
• /
• 제1권1호
• /
• pp.75-96
• /
• 2001

Actual buckling curves are always characterised by the erosion of ideal buckling curves. In case of compact sections this erosion is due to the imperfections, while for thin-walled members, a supplementary erosion is induced by the phenomenon of coupled instabilities. The ECBL approach- Erosion of Critical Bifurcation Load - represents a practical and convenient tool to characterise the instability behaviour of thin-walled members. The present state-of-art paper describes the theoretical background of this method and the applications to cold-formed steel sections in compression and bending. Special attention is paid to the evaluation methods of erosion coefficient and to their validation. The ECBL approach can be also used to the plastic-elastic interactive buckling of thin-walled members, and the paper provides significant results on this line.