Size-dependent effect on biaxial and shear nonlinear buckling analysis of nonlocal isotropic and orthotropic micro-plate based on surface stress and modified couple stress theories using differential quadrature method

The size-dependent effect on the biaxial and shear nonlinear buckling analysis of an isotropic and orthotropic micro-plate based on the surface stress, the modified couple stress theory （MCST）, and the nonlocal elasticity theories using the differential quadrature method （DQM） is presented. Main advantages of the MCST over the classical theory （CT） are the inclusion of the asymmetric couple stress tensor and the consideration of only one material length scale parameter. Based on the nonlinear von Karman assumption, the governing equations of equilibrium for the micro-classical plate consid- ering midplane displacements are derived based on the minimum principle of potential energy. Using the DQM, the biaxial and shear critical buckling loads of the micro-plate for various boundary conditions are obtained. Accuracy of the obtained results is validated by comparing the solutions with those reported in the literature. A parametric study is conducted to show the effects of the aspect ratio, the side-to-thickness ratio, Eringen＇s nonlocal parameter, the material length scale parameter, Young＇s modulus of the surface layer, the surface residual stress, the polymer matrix coefficients, and various boundary conditions on the dimensionless uniaxial, biaxial, and shear critical buckling loads. The results indicate that the critical buckling loads are strongly sensitive to Eringen＇s nonlocal parameter, the material length scale parameter, and the surface residual stress effects, while the effect of Young＇s modulus of the surface layer on the critical buckling load is negligible. Also, considering the size dependent effect causes the increase in the stiffness of the orthotropic micro-plate. The results show that the critical biaxial buckling load increases with an increase in G12/E2 and vice versa for E1/E2. It is shown that the nonlinear biaxial buckling ratio decreases as the aspect ratio increases and vice versa for the buckling amplitude. Because of the most lightweight micro-composite materials with high strength/weight and stiffness/weight ratios, it is anticipated that the results of the present work are useful in experimental characterization of the mechanical properties of micro-composite plates in the aircraft industry and other engineering applications.

Analytical solution approach for nonlinear buckling and postbuckling analysis of cylindrical nanoshells based on surface elasticity theory

The size-dependent nonlinear buckling and postbuckling characteristics of circular cylindrical nanoshells subjected to the axial compressive load are investigated with an analytical approach. The surface energy effects are taken into account according to the surface elasticity theory of Gurtin and Murdoch. The developed geometrically nonlinear shell model is based on the classical Donnell shell theory and the von Karman＇s hypothesis. With the numerical results, the effect of the surface stress on the nonlinear buckling and postbuckling behaviors of nanoshells made of Si and Al is studied. Moreover, the influence of the surface residual tension and the radius-to-thickness ratio is illustrated. The results indicate that the surface stress has an important effect on prebuckling and postbuekling characteristics of nanoshells with small sizes.

Nonlinear buckling finite element analysis of stiffened B-Al plates

Nonlinear buckling behavior of stiffened composite B-Al plates was analyzed by means of finite element analysis(FEA) method. In the method, the composite material was taken as B matrix into which Al fibers were embedded in different configurations. The laminated B-Al material in the form of rectangular plates was subjected to lateral compressive loading. It is observed that stiffeners have significant effect on the buckling behavior of plates under compressive loading and for various geometrical configurations. The stiffeners used in the modeling are one-sided and have rectangular cross-sections. It is found that there are physically important loading intervals and the critical buckling modes make transitions back and forth between stable and unstable states. Bifurcation buckling regions resulting from various configurations of fiber orientations and different plate aspect ratios are determined. The whole analysis is performed by using ANSYS finite element computations. Only the buckling patterns of stiffened plate configurations under simply supported boundary conditions are studied. Distributions of compressive stresses(σx) vs in-plane contractions(u) and compressive stresses(σx) vs out-of plane deflections(δ) are obtained. Nonlinear analysis of the C2 fiber configuration yields the safest critical buckling stress amongst C1, C2, C3 and C4 configurations. It is concluded that FEA method for the nonlinear buckling analysis generates accurate results.

NONLINEAR BUCKLING ANALYSIS OF HYPERBOLIC COOLING TOWER SHELL WITH RING-STIFFENERS

This paper is concerned with a numerical solution of hyperbolic cooling tower shell, a class of full nonlinear problems in solid mechanics of considerable interest in engineering applications. In this analysis, the post-buckling analysis of cooling tower shell with discrete fixed support and under the action of wind loads and dead load is studied. The influences of ring-stiffener on instability load are also discussed. In addition, a new solution procedure for nonlinear problems which is the combination of load increment iteration with modified R-C are-length method is suggested. Finally, some conclusions having important significance for practice engineering are given.

Nonlinear buckling and postbuckling behavior of cylindrical shear deformable nanoshells subjected to radial compression including surface free energy effects

The objective of the present investigation is to predict the nonlinear buckling and postbuckling characteristics of cylindrical shear deformable nanoshells with and without initial imperfection under hydrostatic pressure load in the presence of surface free energy effects.To this end, Gurtin-Murdoch elasticity theory is implemented into the irst-order shear deformation shell theory to develop a size-dependent shell model which has an excellent capability to take surface free energy effects into account. A linear variation through the shell thickness is assumed for the normal stress component of the bulk to satisfy the equilibrium conditions on the surfaces of nanoshell. On the basis of variational approach and using von Karman-Donnell-type of kinematic nonlinearity, the non-classical governing differential equations are derived. Then a boundary layer theory of shell buckling is employed incorporating the effects of surface free energy in conjunction with nonlinear prebuckling deformations, large delections in the postbuckling domain and initial geometric imperfection. Finally, an eficient solution methodology based on a two-stepped singular perturbation technique is put into use in order to obtain the critical buckling loads and postbuckling equilibrium paths corresponding to various geometric parameters. It is demonstrated that the surface free energy effects cause increases in both the critical buckling pressure and critical end-shortening of a nanoshell made of silicon.

Pseudo-beam method for compressive buckling characteristics analysis of space inflatable load-carrying structures

This paper extends Le van＇s work to the case of nonlinear problem and the complicated configuration. The wrinkling stress distribution and the pressure effects are also included in our analysis. Pseudo-beam method is presented based on the inflatable beam theory to model the inflatable structures as a set of inflatable beam elements with a prestressed state. In this method, the discretized nonlinear equations are given based upon the virtual work principle with a 3-node Timoshenko＇s beam model. Finite element simulation is performed by using a 3-node BEAM189 element incorporating ANSYS nonlinear program. The pressure effect is equivalent included in our method by modifying beam element cross-section parameters related to pressure. A benchmark example, the bending case of an inflatable cantilever beam, is performed to verify the accuracy of our proposed method. The comparisons reveal that the numerical results obtained with our method are close to open published analytical and membrane finite element results. The method is then used to evaluate the whole buckling and the loadcarrying characteristics of an inflatable support frame subjected to a compression force. The wrinkling stress and region characteristics are also shown in the end. This method gives better convergence characteristics, and requires much less computation time. It is very effective to deal with the whole load-carrying ability analytical problems for large scale inflatable structures with complex configuration.

Stability Analysis of Long-Span Continuous Rigid Frame Bridge with Thin-Wall Pier

During cantilever cast in construction of high-pier and large-span continuous rigid frame bridges, structural stability in the longest cantilevered stage is very important. Based on a practical design case of a large-span continuous rigid frame bridge in Wuhan, the longest span stability coefficient is calculated with linear-buckling and nonlinear-buckling methods, respectively. The influences of both geometrical nonlinearity and the dual nonlinearity of material and geometry are considered. Numerical results indicate that the nonlinear solution is necessary to stability analysis because linear buckling loads are much higher than those of nonlinear buckling. Thus, the edge fiber yield criterion is more convenient and faster than ultimate loading criterion when estimating nonlinear stability of structure, and can be used easily in the initial engineering design.

Prediction of wrinkles in the membrane

This paper presents an analytical approach for predicting the detailed out-of-plane wrinkle deformation that formed in the membrane. The analytical wrinkle model is based on the assumption that the membrane is able to resist small compressive stress once it has wrinkled. This model is developed for the cases of the rectangular membrane subjected to pure shear and local tension by using the equilibrium equation of the membrane in the deformed configuration. Predictions from this model are compared with the finite element simulation based on the nonlinear buckling finite element method and the results are found to be accurate.

In-Plane Elastic Buckling of Arch

The in-plane elastic buckling behavior of arches is investigated using a new finite-element approach for the nonlinear analysis. The linear buckling, nonlinear primary buckling, and secondary bifurcation buckling behavior of arches are compared taking into account the large deformation and the effects of initial geometric imperfections or perturbations. The theoretical investigation emphasizes the nonlinear secondary bifurcation buckling behavior for a full span uniformly distributed load. The efficiency of compact method for tracing secondary buckling path is shown through several examples. Finally, a new structural design, which prevents the secondary bifurcation buckling by adding some crossed cables across the arch, is proposed to improve the limit load carrying capacity.

Dynamic Response of Tension Plate for UHVDC Transmission Lines Under Ice Shedding Loads

Ice shedding problems have severely threatened the safety of overhead transmission lines and caused enormous ruptures or failures of the conductors and their accessories.It is of great importance to study the dynamic properties of the transmission lines under ice shedding loads.To perform such analysis,the dynamic behavior of two typical strain sections for UHVDC transmission lines under different ice shedding conditions were simulated in this paper.Then,the dynamic response of the key tension plate as well as its buckling properties was analyzed based on the extacted ice shedding results.Finally,laboratory tests were conducted at the China Electric Power Research Institute to assess the critical value of the buckling of the tension plate.The results show that the key tension plate studied in this paper is primarily influenced by the loads along the transmission lines after taking its dynamic response and buckling properties under synthetic ice shedding conditions into consideration.The short-term fluctuation of the tension should be the major focus in tension plate designs.