Damage-Coupled Progressive Failure and Yield Line Analyses of Metal Plates

Continuum damage mechanics based progressive failure analysis of an aluminum alloy AL2024-T3 plate has been carried out. Isotropic continuum damage mechanics model proposed by Chandrakanth and Pandey in 1995 has been implemented in a nonlinear finite element computational scheme based on damage-coupled and damage-uncoupled elastoplastic constitutive relationship. In order to model the progressive growth of damage and plasticity from extreme fibers toward the neutral axis, discrete layered approach has been adopted in the formulation using Ahmed’s degenerate isoparametric shell element, which accounts for shear deformation. A critical damage criteria is used for determining the onset and propagation of failure in the plate. Damage-coupled and damage-uncoupled analyses have been carried out on rectangular and triangular plates of aluminum alloy Al2024-T3. Yield line patterns have been generated using extensive nonlinear progressive failure analysis and comparison with conventional yield line analysis has been made. It is envisioned that employing the methodology presented herein, yield line pattern generation for structural components with complex shapes can be obtained, which would significantly assist engineers in analysis and design of structures.     

Parametric Study on the Dynamic Instability Behavior of Laminated Composite Stiffened Plate

This paper deals with the study of dynamic or parametric instability behavior of laminated composite stiffened plates with step-uniform and concentrated in-plane harmonic edge loading. The eight-noded isoparametric degenerated shell element and a compatible three-noded curved beam element are used to model the plate and the stiffeners, respectively. The method of Hill’s infinite determinant is applied to analyze the dynamic instability regions. Numerical results are presented through convergence and comparison with the published results from the literature. The effects of parameters like loading type, stiffening scheme, lamination scheme, dynamic load factor, and boundary conditions are considered in the dynamic instability analysis of laminated composite stiffened plate. It has been shown that the type of loading and the width of loading have remarkable effect on the dynamic instability characteristics of the stiffened plate.     

Transverse Vibration of Mindlin Plates on Two-Parameter Foundations by Analytical Trapezoidal p-Elements

An analytical trapezoidal hierarchical element for the transverse vibration of Mindlin plates resting on two-parameter foundations is presented. Legendre orthogonal polynomials are used as enriching shape functions to avoid the shear-locking problem and to improve considerably the computational efficiency. Element matrices are integrated in closed form eliminating the numerical integration errors conventionally found. With the C0 continuity requirement, the element can be used to analyze any triangular and polygonal plates without difficulty, while the Kirchhoff p-version elements requiring C1 continuity are not as versatile. The computed natural frequencies for rectangular, skew, trapezoidal, triangular, annular, and polygonal plates on two-parameter foundations show that the convergence of the proposed element is very fast compared to the conventional linear finite elements with respect to the number of degrees of freedom used. Many numerical examples are given.     

Slender Steel Columns Strengthened Using High-Modulus CFRP Plates for Buckling Control

This paper presents the results of an experimental investigation into the behavior of slender steel columns strengthened using high-modulus (313?GPa), carbon fiber-reinforced polymer (CFRP) plates. Eighteen slender hollow structural section square column specimens, 44×44×3.2?mm, were concentrically loaded to failure. The effectiveness of CFRP was evaluated for different slenderness ratios (kL/r), namely, 46, 70, and 93. The maximum increases in ultimate load ranged from 6 to 71% and axial stiffness ranged from 10 to 17%, respectively, depending on kL/r. As kL/r reduced, the effectiveness of CFRP plates also reduced, and failure mode changed from CFRP plate crushing after occurrence of overall buckling, to debonding prior to, or just at, buckling. A simplified analytical model is proposed to predict the ultimate axial load of FRP-strengthened slender steel columns, based on the ANSI/AISC 360-05 provisions, which were modified to account for the transformed section properties and a failure criteria of FRP derived from the experimental results. It was shown that for a given FRP reinforcement ratio, there is a critical kL/r at the low end, below which FRP may not enhance the strength 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.     

Analysis of Hybrid Laminated Composite Plates

Hybrid laminated composite plates are analyzed using a nine‐noded isoparametric plate finite element based on Mindlin's theory. The shear flexibility is included in the finite element modeling. Shear flexibility is of importance, especially when different materials are used in the laminate design. Hybrid laminates consisting of graphite∕epoxy and kevlar∕epoxy plies are considered for illustration. The study indicates that hybrid laminates provide stiffnesses that are intermediate to the values obtained for single‐material laminates. The minimum deflection is achieved at different fiber orientation for thick plates compared to thin plates. The deflection behavior of hybrid laminates seems to be less affected by outer‐ply stiffness in the case of thick plates. Thick plates show less variation in the first natural frequency with fiber orientation but hybridization changes the natural frequency considerably. The first natural frequency of the hybrid laminate can be made higher than the stiffer single‐material laminate.     

Influence of Functionally Graded Material on Buckling of Skew Plates under Mechanical Loads

In this technical note, the critical buckling of simply supported functionally graded skew plate subjected to mechanical compressive loads is evaluated using first-order shear deformation theory in conjunction with the finite element approach. The material properties are assumed to vary in the thickness direction according to the power-law distribution in terms of volume fractions of the constituents. The effective material properties are estimated from the volume fractions and the properties of the constituents using the Mori–Tanaka homogenization method. The effects of aspect ratio, material gradient index, and skew angle on the critical buckling loads of functionally graded material plates are highlighted.     

Dynamic Response of Plates on Elastic Foundation to Moving Loads

A procedure incorporating the finite strip method and a spring system has been developed and applied to treat the dynamic response of plate structure resting on an elastic foundation to moving loads. The response to a single moving concentrated load is first investigated and then the effects of velocity, elastic foundation stiffness, moving path, and distance between multiple moving loads are studied. The response under a moving harmonic load with constant velocity is finally treated and the effect of the load frequency is investigated. Results indicate that the foundation stiffness and the velocity and frequency of the moving load have significant effects on the dynamic response of the plate and on resonant velocities. Some of these findings might find use in practical applications.     

Simple Formulation for the Flexure of Plates on Nonlinear Foundation

Plates resting on an elastic medium are normally analyzed in a simplified way using the linear Winkler foundation approach. Nevertheless, plates resting on layered medium with vast differences in their moduli exhibit nonlinear behavior under pressure. The present technical note deals with a nonlinear finite-element procedure to analyze plates with linear strain displacement relations resting on a nonlinear elastic media. The coupled problem is formulated using the total potential energy (TPE) concept. The nonlinear foundation stiffness matrices have been derived using the Taylor expansion of the TPE at equilibrium and a symbolism of grouping the energy contributions. The nonlinear foundation stiffness matrices derived in the present technical note have been demonstrated to yield results that agree well with published results in the literature. A brief parametric study on the effects of nonlinearity of the foundation is also presented using the proposed foundation stiffness matrices.     

Determination of Physical Parameters of Stiffened Plates using Genetic Algorithm

An investigation on stiffened isotropic and composite plates has been conducted to determine the geometric and material parameters for the plate, as well as the stiffener from experimental modal data and finite element predictions using a genetic algorithm (GA). The problem is formulated as a global minimization of the error function defined by the difference in undamped eigenvalues and eigenvectors, as predicted from the finite-element modeling to that obtained experimentally. The parameter estimation problem is solved using a GA implementing selection, crossover, and mutation operators to obtain the global minimum solution. Because stiffeners contribute substantially to the overall rigidity of the plate assembly, their position, physical properties, and orientation create considerable variation of the modal properties, as compared to the bare plate with similar construction. This makes each of the stiffened plate identification problems rather unique. GAs have been the subject of considerable interest in providing a robust search procedure for a global optimum solution for such difficult minimization problems. The method is demonstrated on a few simulated examples on stiffened plates to investigate the uniqueness and convergence of results. The methodology, although slow in execution, is found to be very robust, even in the presence of noise, for isolating interesting zones of the search space. Unlike many traditional optimization techniques, it does not get stuck at a particular local minimum due to its parallelism.     

Higher-Order Finite Strip Method for Postbuckling Analysis of Imperfect Composite Plates

Postbuckling analysis is essential to predict the capacity of composite plates carrying considerable additional load before the ultimate load is reached, and manufacturing-induced geometric imperfections often reduce the load-carrying capacity of composite structures. A higher-order finite strip method based on the higher-order shear deformation plate theory is developed for postbuckling analysis of laminated composite plates with initial geometric imperfection subjected to progressive end shortening. The arbitrary nature of initial geometric imperfection induced during manufacturing is accounted for in the analysis. Nonlinear equilibrium equations are solved by a Newton-Raphson procedure. Examples of postbuckling analyses of unsymmetric cross-ply, angle-ply, and arbitrary laminates are presented, and the accuracy and performance of the method are examined. The numerical higher-order finite strip method presented can be used as an accurate and efficient tool for postbuckling analysis of imperfect composite plates.     

Analysis of Laminated Sandwich Plates Based on Interlaminar Shear Stress Continuous Plate Theory

The bending response of sandwich plates with stiff laminated face sheets is studied by a six-noded triangular element having seven degrees of freedom at each node. The element formulation is based on a refined higher-order plate theory having all the features for an accurate modeling of sandwich plates with affordable unknowns. The refined plate theory is quite attractive but suffers from a problem concerned with an interelement continuity requirement when it is used in finite element analysis. The problem has been dealt satisfactorily in this new element, which is applied to the analysis of sandwich plates of different kinds.     

Vibration of Pressure Loaded Nonlinear Rectangular Plates with Cross Stiffener

The resonant frequency response of large static pressure loaded, nonlinear rectangular plates with a cross stiffener have been investigated theoretically. The nonlinear Berger equation was solved by applying the finite-difference method. Replacing the partial differential equation governing the small amplitude vibration of static pressure loaded plates and the boundary conditions by the finite-difference equations approximately, the simultaneous, homogeneous, and algebraic equations are obtained. Under the condition that the determinant of coefficient matrix must be equal to zero, the resonant frequencies are determined. The numerical procedure is simpler than the procedures based on the von Kármán theory, and reasonable results are obtained.     

Large-Deflection Mathematical Analysis of Rectangular Plates

A large-deflection mathematical analysis of rectangular plates under uniform lateral loading is presented in this paper. The analysis is based on solving two fourth-order, second-degree, partial differential Von Kármán equations relating the lateral deflections to the applied load. This paper provides a mathematical procedure which benefits from the software and hardware computing capabilities that were unavailable when mathematical modeling was last attempted. The solution is presented in a simple form suitable for direct practical use and can be easily implemented in common spreadsheet packages. Plates with two boundary conditions, namely, simply supported edges and held edges, are considered. Comparisons are held against earlier exact and approximate solutions, including results of finite element analyses. The results show close agreement with other exact analysis methods. The solution is able to produce the same results as other exact solutions, but with a much simpler and a more practical approach.     

Stability Analysis of Composite Plates with Through-the-Width Delamination

In this paper, the compressive bucking and postbuckling behavior of composite laminates with through-the-width delamination are investigated. The analytical method is based on the first-order shear deformation theory, and its formulation is developed on the basis of the Rayleigh-Ritz approximation technique by the implementation of the polynomial series, which has been used for the first time in the case of the mixed mode of buckling. Both local buckling of the delaminated sublaminate and global buckling of the whole plate are investigated. Also, the contact among sublaminates is taken into account. The three-dimensional finite-element analysis is performed by using ANSYS5.4 general-purpose commercial software just to compare the finite-element method results with those obtained by the analytical model. It is noted that the significance and contribution of the current paper lies in the fact that for a rather complicated problem, very good results are obtained by using a fairly small number of degrees of freedom through the application of complete polynomial series.     

Simulation of Soil Behavior under Blast Loading

A viscoplastic cap model was previously developed to address the high strain rate effect on soil behaviors. Although the model is an improvement over the inviscid cap model, it does not update soil density and bulk modulus as the shock wave propagates through the soil. Further, soil should be modeled as a three-phase porous media to accommodate various degrees of water saturation. This is especially true for the soil mass surrounding the source of energy release because each of the three phases responds differently to shock loading. A revised cap model comprising a Gruneisen equation of state for each of the three phases has been developed. These equations of state for solid, water, and air have been integrated with the viscoplastic cap model to simulate behaviors of soil with different degrees of water saturation. Numerical results from this revised soil cap model compared closely with experimental data from explosive tests in both dry and saturated soil.     

Bending of Composite Stiffened Hypar Shell Roofs under Point Load

The present paper applies a combination of an eight noded shell element with a three noded beam element, both curved and isoparametric to solve a bending problem of a composite stiffened hypar shell subjected to a concentrated load. Benchmark problems are solved to validate the suitability of the approach and a wide spectrum of stiffened hypar shell problems are solved by varying the lamination and curvature of simply supported and clamped shell surfaces. Different positions of stiffeners, both in plan and section, are considered together with variation of stiffener depth. Both static deflections and force/moment resultants are examined thoroughly. The performances of the different shell options are studied by arranging them rankwise and through a typical relative performance matrix, which will enable a designer to make a rational choice between a number of options.     

Low-Velocity Impact Dynamic Behavior of Laminated Composite Nonprismatic Folded Plate Structures

In this paper, the higher-order shear deformation theory is used to study the response of graphite/epoxy laminated composite nonprismatic folded plates subjected to impact loads. A finite-element model of the theory is also developed. The modified Hertzian contact law incorporated within the Newton–Raphson method is used to calculate the contact force between the impactor and the laminated plate. For time integration, the Newmark direct integration was adopted. Numerical results are presented to demonstrate the effects of span-to-thickness ratio, fiber angle, stacking sequence, and crank angle on the response of laminated plate subjected to impact. It is demonstrated that the results obtained from the present investigation compare well with those reported in the open literature.     

Moment-Inelastic Rotation Behavior of Longitudinally Stiffened Beams

The significance for inelastic design of moment-inelastic rotation behavior with respect to interior pier sections of steel girder bridges is experimentally investigated. Under center span loading conditions, 12 welded, built-up, simply supported beams with various slenderness ratios of the flange and web plates are tested. In this test, lengths and locations for partial longitudinal stiffeners on the web plates are varied, and the results are then compared with the inelastic deformation capacity of beams without longitudinally stiffened web plates. The results are also compared with the inelastic design code in AASHTO LRFD bridge design specifications. It is concluded that (1) the ultimate strength of stiffened beams is governed by the local buckling at the compression flange of the far end from the loading point due to the presence of a partial longitudinal stiffener; and (2) the inelastic rotation capacity and ultimate strength of a beam with a stiffened web plate are remarkably improved. The optimum length and location of stiffeners on the plates are given.     

Buckling of Laminated Composite Rectangular Plates

The present study estimates the critical/buckling loads of laminated composite rectangular plates under in-plane uniaxial and biaxial loadings. The formulation is based on the first-order shear deformation theory and von-Karman-type nonlinearity. Chebyshev series is used for spatial discretisation and quadratic extrapolation is used for linearization. An incremental iterative approach is used for estimation of the critical load. Different combinations of simply supported, clamped and free boundary conditions are considered. The effects of plate aspect ratio, lamination scheme, number of layers and material properties on the critical loads are studied.