Optimum design of laminated composite under axial compressive load

In the present study optimal design of composite laminates, with and without rectangular cut-out, is carried out for maximizing the buckling load. Optimization study is carried out for obtaining the maximum buckling load with design variables as ply thickness, cut-out size and orientation of cut-out with respect to laminate. Buckling load is evaluated using a ‘simple higher order shear deformation theory’ based on four unknown displacements u, v, w _b and w _s . A C¹ continuous shear flexible finite element based on HSDT model is developed using Hermite cubic polynomial. It is observed that for thick anti-symmetric laminates, the non-dimensional buckling load decreases with increase in aspect ratio and increase in fibre orientation angle. There is a decrease in the non-dimensional buckling load of symmetric laminate in the presence of cut-out.     

Lyapunov stability of columns, pipes and rotating shafts under time-dependent excitation

Structural or mechanical systems governed by non-autonomous partial differential equations are considered. The systems are such that they would be conservative in the absence of dissipation and time variation of the loading parameter. They possess an equilibrium state, and sufficient conditions for its stability are obtained with the use of Lyapunov's direct method. Three problems are treated: a column with a time-varying axial load, a pipe conveying fluid with time-varying velocity, and a rotating shaft with time-varying angular velocity. These excitations appear in coefficients of the equations of motion, and the stability conditions involve the excitations and their time rates of change     

Buckling of composite orthotropic cylindrical shells under non-uniform axial loads

The static buckling of orthotropic composite cylindrical shells, under circumferentially non-uniform axial loads is investigated based on Flügge-type field equations. Use of a complex finite Fourier transform provides a simple method for handling any arbitrary non-uniform load but introduces modal coupling between the transformed equations. For simply supported boundaries (conditions SS3) the determination of the critical buckling load reduces to finding the eigenvalues of a finite matrix. Three different non-uniform loads are considered, having forms proportional to (1 + 2cosθ), cosθ and (θ^* − θ) where is the Heaviside function, θ is the circumferential coordinate and aθ^* is the width of an axially loaded strip of the shell of radius a. Computed results indicate the sensitivity of the critical buckling loads to the type of non-uniform load and the material lay-ups of the cylinders.     

Optimization of composite plates with piezoelectric stiffener-actuators under in-plane compressive loads

Stiffeners which are used to strengthen a plate can be constructed of piezoceramic materials and subsequently used as piezo actuators to improve the load carrying capacity of the plate. In the present study, a fibre composite plate with initial imperfections and under in-plane compressive loads is studied with a view towards minimizing its deflection using the piezo actuators and the fibre orientations. Piezoceramic stiffeners are bonded symmetrically on the top and bottom of the plate and deployed as actuators. Two cases of electric fields, namely, the in-phase and out-of-phase voltages are applied to the actuators. The presence of initial deflections leads to deformation under the in-plane compressive loads which should be less than the critical buckling load. Two cases of initial imperfections are considered, and the first one is the deterministic initial deflections which are known a priori and as such they are given as input parameters for the problem. In the second case the initial deflections are uncertain and they have to be obtained according to a given criterion. In the present study they are determined to produce the least favourable initial deflection (largest deflection) at a given point and the solution is obtained by convex modelling. The effect of the actuators, the ply angles and the voltage are studied and their effects on the transverse deflection are investigated. A performance index involving the L₂ norm of the deflections is minimized using the piezo effect and as well as the ply angles the optimal values of which are determined for various problem parameters.     

The stability of composite material stiffened conical shells under axial compression

The stability of composite material stiffened conical shells under uniform axial compression and with classical clamped boundary conditions is investigated. The effects of stiffeners are uniformly distributed over the whole surface of the shell, and the shell is treated as an equivalent orthotropic shell. A method of solution is developed by using energy principles and Rayleigh-Rize approximations. It is shown that the approach proposed in this paper is practical, effective and satisfactory.     

Non‐linear dynamic stability analysis of composite laminates under periodic in‐plane compressive loads

This work deals with the investigation of the non‐linear instability behaviour of the composite laminates subjected to periodic in‐plane/axial load, through the finite element formulation with dynamic response analysis. Here, C¹ eight‐noded shear‐flexible plate element, based on a new kind of kinematics which allows to exactly ensure the continuity conditions for displacements and stresses at the interfaces between the layers of the laminate, and also the boundary conditions at the top and bottom surfaces of the laminate, is employed. The non‐linear governing equations obtained are solved using the Newmark direct integration method coupled with a modified Newton–Raphson iteration procedure. The analysis brings out various characteristic features of the dynamic stability such as existence of beats, their dependency on the forcing frequency, and the typical character of vibrations in the different regions. Numerical results are also presented to highlight the influence of ply‐angle and lay‐up of the laminate on dynamic stability behaviour of the composite laminates. Copyright © 1999 John Wiley & Sons, Ltd.     

Dynamic stability analysis of laminated composite cylindrical shells subjected to conservative periodic axial loads

The dynamic stability of thin, laminated cylindrical shells under combined static and periodic axial forces is studied here using Love's theory for thin shells. A system of Mathieu–Hill equations is obtained by a normal-mode expansion of the equations of motion, the stability of which is examined by Bolotin's method. The dynamic instability regions are investigated for different lamination schemes. The effects of the length-to-radius and thickness-to-radius ratios of the cylinder on the instability regions are also examined.     

Dynamic stability of linear parametrically excited twisted Timoshenko beams under periodic axial loads

In this paper, the parametric instability of twisted Timoshenko beams with various end conditions and under an axial pulsating force is studied. The equations of motion in the twisted frame are derived using a finite element method. Based on Bolotin??s method, a set of second-order ordinary differential equations with periodic coefficients of Mathieu?CHill type is formed to determine the instability regions for twisted Timoshenko beams. A dynamic instability index is defined and used as an instability measure to study the influence of various parameters. The effects of beam length, inertia ratio, pre-twist angle, dynamic component of axial force and restraint condition on the instability regions and dynamic instability index of the twisted beam are investigated and discussed.     

Concrete columns confined by fiber composite wraps under combined axial and cyclic lateral loads

This paper presents nonlinear finite element analysis of fiber reinforced polymer (FRP) jacketed reinforced concrete columns under combined axial and cyclic lateral loadings. Large-scale control and FRP-wrapped reinforced concrete columns (762 mm in diameter and 4978 mm in height) were modeled using the nonlinear finite element analysis software MARC™. The models were capable of allowing for the degradation of the stiffness under cyclic loading. The finite element analysis results indicated that reinforced concrete columns externally wrapped with the FRP fabric in the potential plastic hinge location at the bottom of the column showed significant improvement in both strength and ductility capacities, and the FRP jacket could be used to delay the degradation of the stiffness of reinforced concrete columns.     

复合材料薄壁管冲击断裂分析与吸能特性优化

为实现不同冲击载荷下的吸能管结构逆向设计, 应用复合材料强度和刚度理论, 计算得到树脂基纤维增强复合材料正交各向异性的力学参数, 同时应用非线性显式有限元算法模拟了轴向冲击载荷作用下管件的动态断裂过程。根据正交设计原理, 得到了管件比吸能与其几何参数之间的非线性映射关系, 并构造出了相应的响应表面。按照汽车正面碰撞对冲击加速度的要求, 应用序列二次规划算法对吸能管进行了优化设计, 得到了具有较优吸能效率和较小冲击力峰值的吸能管结构参数。结果显示: 方管的变形模式、吸能量、冲击载荷-位移曲线变化趋势、冲击载荷峰值等与试验结果吻合很好; 当管件的壁厚、截面长度、管长分别选取2.1、44、200 mm时, 可得到设计域内的最大比吸能29.23 J/g。      

Failure behavior of three-axis woven carbon/carbon composites under compressive and transverse shear loads

This work examines the responses of three-dimensional carbon/carbon composites under axial compression and transverse shear. By using a 3D weaving technique, two types of preforms with different bundle sizes of the weaving yarns were prepared for assessing its influence on the failure behavior. Carbon yarns were arranged in a three-axis, orthogonal form with interlacing loops on outer surfaces. The carbon matrix was added by using a phenolic resin as the matrix precursor. Resin transfer molding was used for resin impregnation, followed by the curing and carbonization of the resin. The matrix filling was repeated up to five cycles, and the efficiency of the matrix filling was examined. Special fixtures were designed for applying the loads to the 3D composites. Microscopic observations on the induced damage were carried out. The axial yarns were found to undergo bending fracture in the compressive tests. The yarn imperfection, rather than the fiber misalignment, was the major failure-determining factor. The bending of the yarns is analyzed, and the critical value of imperfection that leads to bending fracture is given. The transverse shear resulted in complex but intriguing damage modes, which are closely related to the surface loops and through-thickness yarns. Some keys for preform design to best withstanding the shear are discussed.     

Postbuckling of nanotube-reinforced composite cylindrical shells under combined axial and radial mechanical loads in thermal environment

A postbuckling analysis is presented for nanocomposite cylindrical shells reinforced by single-walled carbon nanotubes (SWCNTs) subjected to combined axial and radial mechanical loads in thermal environment. Two types of carbon nanotube-reinforced composite (CNTRC) shells, namely, uniformly distributed (UD) and functionally graded (FG) reinforcements, are considered. The material properties of FG-CNTRCs are assumed to be graded in the thickness direction, and are estimated through a micromechanical model. The governing equations are based on a higher order shear deformation shell theory with a von Kármán-type of kinematic nonlinearity. The thermal effects are also included and the material properties of CNTRCs are assumed to be temperature-dependent. A boundary layer theory and associated singular perturbation technique are employed to determine the buckling loads and postbuckling equilibrium paths. The numerical illustrations concern the postbuckling behavior of perfect and imperfect, FG-CNTRC cylindrical shells under combined action of external pressure and axial compression for different values of load-proportional parameters. The results for UD-CNTRC shell, which is a special case in the present study, are compared with those of the FG-CNTRC shell.     

Control of load/displacement responses of AA6061-T6 and T4 circular extrusions under axial compressive loads

Axial crushing of AA6061-T6 and T4 circular extrusions with variable wall thicknesses was completed under both dynamic and quasi-static loading conditions to investigate the capability of controlling the load/displacement responses of the extrusions. Circular specimens with a nominal original wall thickness of 3.175 mm, an outer diameter of 50.8 mm, and a length of 300 mm were considered. Variations of the wall thickness in the axial direction were completed by material removal from the extrusion sidewall prior to crushing tests. Cutters used in this research had a height of 20 mm and blade tip widths of 1.0 mm. A curved deflector was used to flare the cut petalled sidewalls and facilitate the cutting system. Results from the impact tests illustrated that an initial peak cutting force with a magnitude of 1.08-1.74 times higher than that for the quasi-static loading was needed to initiate the cutting deformation mode. After this transient cutting stage, the load/displacement responses were observed to be similar to that from the quasi-static tests except for some slight fluctuations resulting from a minor amount of material fracture which occurred on the petalled sidewalls. A lesser extend of material fracture was observed on the T4 temper specimens due to the work hardening material property of the T4 temper condition. The mean cutting force from the dynamic tests were determined to be in the range of 0.92-1.09 times the mean force from the corresponding quasi-static test. Control of load versus displacement responses of the extrusions under both impact and quasi-static compressive loading conditions was accomplished through the variation of the wall thickness along the axial direction of extrusions.     

Strength of composite laminates under biaxial loads

Five well known failure criteria and one simple progressive model have been used in conjunction with laminate theory, which allows for nonlinear lamina shear behaviour, to predict the initial and final failure strengths of filament wound composite tubes. The predictions have been compared with experimental leakage and fracture stresses for ±75°, ±55° and ±45° filament wound GRP tubes subjected to a wide range of biaxial stress systems including biaxial compression. In some cases the fracture strengths were a factor of 10 higher than the initial failure predictions. The simple progressive failure theory predictions gave the best agreement with the experimental results.©British Crown Copyright 1996, Defence Evaluation and Research Agency published by Kluwer Academic Publishers with permission.     

Crushing behaviour of composite hemispherical shells subjected to quasi-static axial compressive load

This paper examines the effects of composite constituents and geometry on the energy absorption capability of composite hemispherical shells. To examine the effects of matrix types on their energy absorption capability, glass fibre/epoxy and glass fibre/polyester hemispherical shells were fabricated. While glass fibre/epoxy and carbon fibre/epoxy hemispherical shells were fabricated to investigate the effect of fibre reinforcements. Effect of aspect ratio (R/t) was also examined and the results were presented. The results obtained showed that the energy absorption capability of the hemispherical shells significantly affected by the composite constituents as well as R/t ratio.