Postbuckling of Pressure-Loaded Functionally Graded Cylindrical Panels in Thermal Environments

A postbuckling analysis is presented for a functionally graded cylindrical panel of finite length subjected to lateral pressure in thermal environments. Material properties are assumed to be temperature dependent, and graded in the thickness direction according to a simple power-law distribution in terms of the volume fractions of the constituents. The governing equations of a functionally graded cylindrical panel are based on Reddy’s higher-order shear deformation shell theory with von Kármán–Donnell-type of kinematic nonlinearity and include thermal effects. The two straight edges of the panel are assumed to be simply supported and two curved edges are either simply supported or clamped. The nonlinear prebuckling deformations and initial geometric imperfections of the panel are both taken into account. A boundary layer theory of shell buckling, which includes the effects of nonlinear prebuckling deformations, large deflection in the postbuckling range, and initial geometric imperfections of the shell, is extended to the case of functionally graded cylindrical panels. A singular perturbation technique is employed to determine the buckling loads and postbuckling equilibrium paths. The numerical illustrations concern the postbuckling behavior of simply supported, pressure-loaded, perfect and imperfect, functionally graded cylindrical panels with two constituent materials under different sets of thermal environments. The influences played by temperature rise, volume fraction distributions, transverse shear deformation, panel geometric parameters, as well as initial geometric imperfections, are studied.     

Thermomechanical Postbuckling Analysis of Cross-Ply Laminated Cylindrical Shell Panels

The postbuckling analysis of symmetric and antisymmetric cross-ply laminated cylindrical shell panels subjected to thermomechanical loading is examined in this paper. The formulation is based on an extension of Reissner’s shallow shell simplifications and accounts for parabolic distribution of transverse shear strains. Adopting a multiterm Galerkin’s method, the governing nonlinear partial differential equations are reduced into a set of nonlinear algebraic equations. The nonlinear equilibrium paths through limit points are traced using the Newton–Raphson method in conjunction with Riks approach. Numerical results are presented for symmetric [?start0/90/0end?] and antisymmetric [?start0/90end?] cross-ply laminated cylindrical shell panels, that illustrate the influence of mechanical edge loads, lateral distributed load, initial imperfection, and temperature field on the limit loads and snap-through behavior.     

Postbuckling Response Simulations of Laminated Anisotropic Panels

Numerical simulations are used in conjunction with experiments to study the buckling and postbuckling responses and failure initiation of flat, unstiffened composite panels. The numerical simulations are conducted using two‐dimensional shear‐flexible finite elements. The effect of the laminate stacking sequence on the buckling and postbuckling responses is studied. Correlation between numerical and experimental results is good through buckling, but the numerical models overestimate the postbuckling stiffness of the panels when nominal values of the material properties are used. To explain the discrepancies in the postbuckling stiffnesses, analytic sensitivity derivatives are calculated and used to study the sensitivity of the buckling and postbuckling responses to variations in different material and lamination parameters. Experimental results indicate that failure occurs along a nodal line. Numerical results show that the location of failure initiation corresponds to that of the maximum transverse shear‐strain energy density in the panel, which occurs at the edge of the panel at a nodal line. However, the transverse shear deformation has a negligible effect on the global response characteristics of the panel.     

Dynamic Thermal Buckling of Functionally Graded Spherical Caps

In the present work, dynamic buckling behavior of clamped functionally graded spherical caps suddenly exposed to a thermal field is studied using the finite-element procedure. The material properties are graded in the thickness direction. The temperature load corresponding to a sudden jump in the maximum average displacement in the time history of the shell structure is taken as the dynamic buckling temperature. Numerical study is carried out to highlight the influences of shell geometries and material gradient index on the critical buckling temperature.     

Vibration of Axially Loaded Rotating Cross-Ply Laminated Cylindrical Shells via Ritz Method

This paper presents the free vibration analysis of axially loaded rotating cross-ply laminated cylindrical shells with the consideration of the effects of centrifugal and Coriolis forces as well as the initial hoop tension due to the rotation. The Ritz method is employed for the solution of this problem. Adopting the trigonometric series as the admissible displacement functions, a set of frequency characteristics equations is derived. The frequency characteristic analysis for shells of simply supported boundary conditions is examined and the frequency characteristics of various lamination schemes are investigated. The results from the present analysis are compared with the available solutions to validate its accuracy.     

Thermal Effect on the Postbuckling Behavior of an Elastic or Elastoplastic Truss

Temperature rise may lead to strength degradation and stiffness deterioration of structures under fire conditions. The purpose of this paper is to theoretically study the thermal effect on the postbuckling behavior of an elastic or elastoplastic two-member truss, based on large-deformation elasticity considerations. Two kinds of loadings are considered, i.e., trusses under constant temperature but increasing loads, and trusses under constant loads but rising temperature. For the case with constant temperature, the critical load of an elastic truss will be greatly reduced if the effect of yielding is taken into account. Moreover, yielding of material can cause the truss to bifurcate from the original elastic path. For the case with constant loads, a critical temperature that occurs as the limit point of the temperature–deflection curve can always be found. Besides, the presence of yielding can drastically reduce the critical temperature of an elastic truss, causing it to collapse in an abrupt manner. The solutions presented herein can be used as benchmarks for calibration of the accuracy of general finite-element procedures in analyzing structures under fire conditions.     

Thermal Postbuckling of Laminated Composite Plates with Temperature Dependent Properties

The paper deals with the theoretical investigation of the postbuckling of laminated composite rectangular plates subjected to uniform in-plane temperature. An analytical method based on Chebyshev polynomial is employed. The formulation is based on Reissner–Mindlin plate theory and von Kármán nonlinear kinematics. The resulting nonlinear coupled differential equations are linearized using quadratic extrapolation technique. Double Chebyshev finite series is used to discretize the differential equations. An incremental iterative approach is employed for the solution. The effects of temperature dependent mechanical and thermal properties on the limiting/critical temperature and the postbuckling response are studied. The numerical results for different boundary conditions and lamination schemes are presented. Analysis results indicate that temperature dependent properties reduce the critical/limiting temperature and postbuckling strength.     

Buckling Analysis of Nonuniform and Axially Graded Columns with Varying Flexural Rigidity

In this paper, we present a novel analytic approach to solve the buckling instability of Euler-Bernoulli columns with arbitrarily axial nonhomogeneity and/or varying cross section. For various columns including pinned-pinned columns, clamped columns, and cantilevered columns, the governing differential equation for buckling of columns with varying flexural rigidity is reduced to a Fredholm integral equation. Critical buckling load can be exactly determined by requiring that the resulting integral equation has a nontrivial solution. The effectiveness of the method is confirmed by comparing our results with existing closed-form solutions and numerical results. Flexural rigidity may take a majority of functions including polynomials, trigonometric and exponential functions, etc. Examples are given to illustrate the enhancement of the load-carrying capacity of tapered columns for admissible shape profiles with constant volume or weight, and the proposed method is of benefit to optimum design of columns against buckling in engineering applications. This method can be further extended to treat free vibration of nonuniform beams with axially variable material properties.     

Behavior of Axially Loaded Pile Groups Driven in Clayey Silt

This paper presents a case history describing measurements made during the installation and load testing of groups of five, closely spaced, precast concrete piles in a soft clay-silt. The test results extend the presently limited set of reported high-quality data for pile groups at field scale and allow assessment of the reliability of existing numerical and analytical predictive approaches. Full scale maintained compression and tension load tests on groups as well as tests on single (reference) piles and an individual test on a pile within a pile group enable the effects of multiple pile installations and interaction between piles under load to be assessed. The results are compared with existing simple methods of pile group analysis and with other case histories reporting results on small pile groups. A simple expression to evaluate pile group stiffness efficiency is proposed.     

Novel Formulation to Study Thermal Postbuckling of Circular Plates with Edges Elastically Restrained against Rotation

A novel formulation is used to study the thermal postbuckling behavior of circular plates, with the edges supported to not have lateral deflection and elastically restrained against rotation. The elastic restraint is mathematically represented by an elastic rotational spring. The circular plate is subjected to a uniform edge compressive radial load, developed because of a uniform temperature rise. The formulation is on the basis of on the radial tensile load developed in the plate because of the large deflections of the plate with edges immovable in the plane normal to the edge and the linear buckling load corresponding to the uniform edge radial compressive load. The developed radial tensile load is obtained by using Berger’s approximation. The numerical results obtained from the present investigation in terms of the ratios of the postbuckling to the buckling loads for several rotational spring stiffness values compare well with those obtained by using the versatile finite-element analysis.     

Uplift Capacity of Axially Loaded Piles in Clays

The present study aims at determining the uplift capacity of axially loaded piles in clays whose undrained cohesion increases linearly with depth. With the application of the axisymmetric static limit analysis approach, proposed recently by the writers, the variation of the nondimensional uplift factors with respect to changes in the embedment ratio (H/B) has been obtained for several rates of increase of soil cohesion with depth defined in terms of a nondimensional factor m for given values of soil cohesion (c0) along the ground surface and diameter (B) of pile. The uplift resistance has been evaluated in the form of the uplift factors, Fcb and Fct due to the components of the shaft resistance and the total resistance, respectively. For the given values of c0 and B, the magnitude of the uplift resistance increases continuously with an increase in the value of m. Furthermore, the Fcb values are found to remain unaffected with the variation in the shaft adhesion, whereas, the Fct values increase continuously with an increase in the adhesion factor of the pile shaft.     

Performance of Axially Loaded Short Rectangular Columns Strengthened with Carbon Fiber-Reinforced Polymer Wrapping

This paper presents results of a comprehensive experimental investigation on the behavior of axially loaded short rectangular columns that have been strengthened with carbon fiber-reinforced polymer (CFRP) wrap. Six series, a total of 90 specimens, of uniaxial compression tests were conducted on rectangular and square short columns. The behavior of the specimens in the axial and transverse directions is investigated. The parameters considered in this study are (1) the concrete strength; (2) the aspect ratio of the cross section; and (3) the number of CFRP layers. The findings of this research can be summarized as follows: The CFRP wrapping enhances the compressive strength and the ductility of both square and rectangular columns, but to a lesser degree than that of circular columns. The ultimate strength and the ductility of the CFRP confined concrete increase with increasing number of confining layers. The increase in strength and ductility is more significant for lower strength concrete, representing poor or degraded concrete, than for normal-to-high strength concrete; that is, the maximum gain in strength that can be achieved for 3 ksi concrete wrapped columns is approximately 90%, as compared to only 30% for 6 ksi concrete wrapped columns. The CFRP confining jacket must be sufficiently stiff to develop appropriate confining forces at relatively low axial strain levels. The gain in compressive strength obtained by the CFRP confined concrete depends mainly on the relative stiffness of the CFRP jacket to the axial stiffness of the column.     

Thermal Buckling Analysis of SMA Fiber-Reinforced Composite Plates Using Layerwise Model

Thermal buckling analysis of laminated smart composite plates subjected to uniform temperature distribution has been presented. Shape memory alloy (SMA) fibers whose material properties depend on temperature have been used as a smart material. A three-dimensional layerwise plate model has been employed in developing the system equations using variational approach. Finite-element method has been adopted for discretization of the laminate. Lagrangian interpolation functions have been used to approximate the displacement components along the thickness as well as in the in-plane direction. The actual variation of prebuckling stresses has been accounted for in the derivation of the geometric stiffness matrix of the laminates. An incremental load technique has been used in the analysis to take into account the nonlinearity in the material properties of the SMA arising due to their temperature dependence. The effects of thickness ratio, orthotropic ratio, fiber orientation, aspect ratio, stacking sequence and various boundary conditions on the critical buckling temperature have been examined in details. The results have been validated with those available in the literature.     

Influence of Route Direction on Thermal Field of Embankments Constructed in High-Altitude Permafrost Area

This paper discusses the effect of route direction, embankment height, and pavement type on the thermal field of embankments built in permafrost regions. A finite-element model (FEM) is adopted to simulate diverse conditions of the embankment. The 30-year meteorological data including the solar radiation, air temperature, and wind velocity are used as the boundary conditions for the Qinghai-Tibet Highway. The results obtained from the FEM calculations are found to be in good agreement with the actual measurements on the thermal field. Further, the results show that route direction has great impact on the equilibrium of the thermal field within embankments in permafrost regions. The thermal imbalance is more obvious for embankments in the east–west direction and less in the north–south direction. In addition, the thermal asymmetry is closely related to seasonal variation and it is more pronounced in winter and less in summer.