Collapse of Composite Rings Due to Delamination Buckling Under External Pressure

The collapse of cylindrical shells under external pressure is known to be controlled by global elastic buckling, material failure, or a combination thereof. In the case of composites, delamination is another factor affecting the stiffness and stability of the structural component. Thin inner delaminated layers are expected to locally buckle inwards, under hoop compression, reducing the effective thickness of the ring wall. This may lead to a premature collapse of composite rings. The problem is numerically treated and parametrically studied. A Fourier series-based finite-element model is formulated for delaminated composite tubular cross sections. A special “chord length” procedure is developed to enable the convergence of the local buckling solution in quasi-static nonlinear analysis. Parametric studies are conducted to assess the influence of delamination length, depth, location, out-of-roundness imperfection, and ring layup on the pressure levels at delamination buckling and collapse.     

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.     

Free-Edge and Ply Cracking Effect in Angle-Ply Laminated Composites Subjected to In-Plane Loads

This paper presents a semianalytical method for the prediction of interlaminar stresses and displacements near the free edges and ply cracks in general angle-ply laminates subjected to biaxial extensions and/or in plane shear deformation. The method is based on a state space representation of the three-dimensional equations of elasticity. Numerical solutions are obtained by using layer refinement in the through thickness direction and Fourier series expansion in the other directions. By this approach, an angle-ply laminate may be composed of an arbitrary number of monoclinic layers and each layer may have different material property and thickness. This method guarantees continuous fields of all interlaminar stresses across interfaces between material layers. Numerical results are compared with those obtained from other methods. It is found that the theory provides a satisfactory approximation to the stress singularities near the free edges and ply cracks. Numerical solutions for antisymmetric laminates under extension and general laminates under shearing are new in the literature and can be used as benchmarks for validating new models.     

Localized Buckling of a Bilinear Elastic Ring under External Pressure

A fully nonlinear finite element analysis for prediction of localization in moderately thick imperfect rings under applied hydrostatic pressure is presented. The present nonlinear finite element solution methodology includes all the nonlinear terms in the kinematic equations and utilizes the total Lagrangian formulation in the constitutive equations and incremental equilibrium equations. A curved six-node element, based on an assumed quadratic displacement field (in the circumferential coordinate), employs a two-dimensional hypothesis, known as linear displacement distribution through thickness theory, to capture the effect of the transverse shear/normal (especially, shear) deformation behavior. The driving factor behind this analysis is to determine the onset of localization arising out of the bilinear material behavior of the ring with modal imperfection. Numerical results suggest that material bilinearity is primarily responsible for the appearance of a limit or localization (peak pressure) point on the postbuckling equilibrium path of an imperfect ring.     

Imperfection Sensitivity of Laminated Cylindrical Shells According to Different Shell Theories

The imperfection sensitivity of laminated cylindrical shells is considered—via the initial postbuckling analysis—on the basis of three different shell theories: Donnell in 1933; Sanders in 1963; and Timoshenko in 1961. The procedure involves nonlinear partial differential equations, which are converted into a sequence of three linear sets. The equations are solved with the variables expanded in Fourier series in the circumferential direction and in finite differences in the axial directions. A general code is developed and used in studying the effect of higher exactness of the shell theory on the sensitivity behavior, and in a parametric study of the sensitivity of anisotropic angle-ply cylindrical shells.     

Nonlinear Response of Laminated Cylindrical Shell Panels Subjected to Thermomechanical Loads

The nonlinear response of multi-layered composite cylindrical shell panels subjected to thermomechanical loads are studied in this article. The structural model is based on the first order shear deformation theory incorporating geometric nonlinearities. The nonlinear equilibrium paths are traced using the arc-length control algorithm within the framework of finite element method. Hashin’s failure criterion has been adopted to predict the first-ply failure of cylindrical laminates. Both temperature independent and temperature dependent elastic properties are considered in the analysis. Specific numerical results are reported to show the effect of radius-to-span ratio, thickness-to-span ratio, laminate stacking sequence, and boundary condition on stability characteristics of laminated cylindrical shell panels subjected to combined thermal and mechanical transverse loads.     

Closed-Form Solutions for Buckling of Long Anisotropic Plates with Various Boundary Conditions under Axial Compression

Closed-form solutions for buckling of long plates with flexural/twist anisotropy with the short edges simply supported and with the longitudinal edges simply supported, clamped, or elastically restrained in rotation under axial compression are presented. An energy method (Rayleigh–Ritz) is employed to obtain the critical buckling loads. The critical buckling loads are expressed in terms of minimum nondimensional buckling coefficients and stiffness parameters. The new closed-form solutions show an excellent agreement when compared to existing solutions and finite-element analysis. Due to their simplicity and accuracy, the new closed-form solutions can be confidently used as an alternative to computationally expensive structural analysis to assess buckling in the preliminary design phase of composite structures.     

Application of an Anisotropic Constitutive Model for Structured Clay to Seismic Slope Stability

The anisotropic nature of response and degradation of shear strength from the undisturbed condition to the remolded state are two fundamental and challenging aspects of response in some clay deposits. This paper presents a comprehensive, yet flexible and practical, version of the SANICLAY model and its application to a seismic slope-stability problem. The model is based on the well-known isotropic modified Cam-Clay model with two additional mechanisms to account for anisotropy and destructuration. The model has been efficiently implemented in a three-dimensional (3D) continuum, coupled, dynamic, finite-difference program. The program has been used to analyze the seismic response of clay slopes to gain better insight into the role of the previously mentioned parameters in real applications. Different aspects of the model, including anisotropy and destructuration, and their effects on the earthquake-induced strains and deformations in the slope have then been explored and presented. By providing a link between the model parameters and the soil’s undrained shear strength, which is a well-known engineering parameter, a benchmark comparison has been made between the results of the present advanced model and those of an engineering approach. To this end, a modified Newmark sliding-block analysis has been used, in which the yield acceleration is gradually reduced as block sliding progresses during the earthquake. It is observed that although the two analyses display the same trends, the modified Newmark sliding-block method provides conservative results compared with those obtained from the developed simulation model.     

Buckling and Postbuckling Behavior of Cross-Ply Composite Plate Subjected to Nonuniform In-Plane Loads

This paper presents a study of buckling and postbuckling behaviour of simply supported composite plates subjected to nonuniform in-plane loading. The mathematical model is based on higher order shear deformation theory incorporating von Kármán nonlinear strain displacement relations. Because the applied in-plane edge load is nonuniform, in the first step the plane elasticity problem is solved to evaluate the stress distribution within the prebuckling range. Using these stress distributions, the governing equations for postbuckling analysis of composite plates are obtained through the theorem of minimum potential energy. Adopting Galerkin’s approximation, the governing nonlinear partial differential equations are reduced into a set of nonlinear algebraic equations in the case of postbuckling analysis, and homogeneous linear algebraic equations in the case of buckling analysis. The critical buckling load is obtained from the solution of associated linear eigenvalue problem. Postbuckling equilibrium paths are obtained by solving nonlinear algebraic equations employing the Newton-Raphson iterative scheme. Explicit expressions for the plate in-plane stress distributions within the prebuckling range are reported for isotropic and composite plates subjected to parabolic in-plane edge loading. Buckling loads are determined for three plate aspect ratios (a/b = 0.5, 1, 1.5) and three different types of in-plane load distributions. The effect of shear deformation on the buckling loads of composite plate is reported. The present buckling results are compared with previously published results wherever possible.     

Micromechanical Explanation of Elasticity and Strength of Gypsum: From Elongated Anisotropic Crystals to Isotropic Porous Polycrystals

Gypsum is made up of interlocked and elongated crystals. The random nature of its morphology suggests to resort to homogenization of random media to investigate its mechanical properties from the scale of the single crystals upwards. Unfortunately, the usual homogenization schemes fail to quantitatively predict the influence of the porosity on the effective Young’s modulus of gypsum. This is clearly due to the inability of such approaches to take into account the elongated nature of the crystals. A modification of the classical self-consistent scheme is proposed. It is validated against elastic characteristics computed by finite element analyses, and also against experiments on real dried gypsum samples (with empty pores). Finally, a strength model based on brittle failure is presented. The whole strength domain in the space of macroscopic principal stresses is derived. The comparison to experimental data in both simple tension and simple compression is remarkably good.     

Application of Optical Measurement Techniques to Supersonic and Hypersonic Aerospace Flows

Experimental investigation is essential to improve the understanding of aerospace flows. During the last years, effort has been put on the development of optical diagnostics capable of imaging or yielding data from the flow in a nonintrusive way. The application of some of these techniques to supersonic and hypersonic flows can be highly challenging due to the high velocity, strong gradients, and restricted optical access generally encountered. Widely used qualitative and semiquantitative optical flow diagnostics are shadowgraph, schlieren, and interferometry. Laser-based techniques such as laser Doppler anemometry and particle image velocimetry are well established for investigation of supersonic flows, but as yet their use in hypersonic flows has been limited. Other relevant measurement techniques include particle tracking velocimetry, Doppler global velocimetry, laser-two-focus anemometry, background oriented schlieren and laser induced fluorescence methods. This paper reviews the development of these and further optical measurement techniques and their application to supersonic and hypersonic aerospace flows in recent years.     

Dynamic Modal Analysis and Stability of Cantilever Shear Buildings: Importance of Moment Equilibrium

The dynamic modal analysis (i.e., the natural frequencies, modes of vibration, generalized masses, and modal participation factors) and static stability (i.e., critical loads and buckling modes) of two-dimensional (2D) cantilever shear buildings with semirigid flexural restraint and lateral bracing at the base support as well as lumped masses at both ends and subjected to a linearly distributed axial load along its span are presented using an approach that fulfills both the lateral and moment equilibrium conditions along the member. The proposed model includes the simultaneous effects and couplings of shear deformations, translational and rotational inertias of all masses considered, a linearly applied axial load along the span, the shear force component induced by the applied axial force as the member deforms and the cross section rotates, and the rotational and lateral restraints at the base support. The proposed model shows that the stability and dynamic behavior of 2D cantilever shear buildings are highly sensitive to the coupling effects just mentioned, particularly in members with limited rotational restraint and lateral bracing at the base support. Analytical results indicate that except for members with a perfectly clamped base (i.e., zero rotation of the cross sections), the stability and dynamic behavior of shear buildings are governed by the flexural moment equation, rather than the second-order differential equation of transverse equilibrium or shear-wave equation. This equation is formulated in the technical literature by simply applying transverse equilibrium “ignoring” the flexural moment equilibrium equation. This causes erroneous results in the stability and dynamic analyses of shear buildings with base support that is not perfectly clamped. The proposed equations reproduce, as special cases: (1) the nonclassical vibration modes of shear buildings including the inversion of modes of vibration when higher modes cross lower modes in shear buildings with soft conditions at the base, and the phenomena of double frequencies at certain values of beam slenderness (L/r); and (2) the phenomena of tension buckling in shear buildings. These phenomena have been discussed recently by the writer (2005) in columns made of elastomeric materials.