Showing papers in "Journal of Engineering Mechanics-asce in 1997"

Phenomenological model for magnetorheological dampers

Abstract: Semiactive control devices have received significant attention in recent years because they offer the adaptability of active control devices without requiring the associated large power sources. Magnetorheological (MR) dampers are semiactive control devices that use MR fluids to produce controllable dampers. They potentially offer highly reliable operation and can be viewed as fail-safe in that they become passive dampers should the control hardware malfunction. To develop control algorithms that take full advantage of the unique features of the MR damper, models must be developed that can adequately characterize the damper's intrinsic nonlinear behavior. Following a review of several idealized mechanical models for controllable fluid dampers, a new model is proposed that can effectively portray the behavior of a typical MR damper. Comparison with experimental results for a prototype damper indicates that the model is accurate over a wide range of operating conditions and is adequate for control design an...

Structural control: past, present, and future

Abstract: This tutorial/survey paper: (1) provides a concise point of departure for researchers and practitioners alike wishing to assess the current state of the art in the control and monitoring of civil engineering structures; and (2) provides a link between structural control and other fields of control theory, pointing out both differences and similarities, and points out where future research and application efforts are likely to prove fruitful. The paper consists of the following sections: section 1 is an introduction; section 2 deals with passive energy dissipation; section 3 deals with active control; section 4 deals with hybrid and semiactive control systems; section 5 discusses sensors for structural control; section 6 deals with smart material systems; section 7 deals with health monitoring and damage detection; and section 8 deals with research needs. An extensive list of references is provided in the references section.

Multisurface Interface Model for Analysis of Masonry Structures

Abstract: The performance of an interface elastoplastic constitutive model for the analysis of unreinforced masonry structures is evaluated. Both masonry components are discretized aiming at a rational unit-joint model able to describe cracking, slip, and crushing of the material. The model is formulated in the spirit of softening plasticity for tension, shear and compression, with consistent treatment of the intersections defined by these modes. The numerical implementation is based on modern algorithmic concepts such as local and global Newton-Raphson methods, implicit integration of the rate equations and consistent tangent stiffness matrices. The parameters necessary to define the model are derived from microexperiments in units, joints, and small masonry samples. The model is used to analyze masonry shear-walls and is capable of predicting the experimental collapse load and behaviour accurately. Detailed comparisons between experimental and numerical results permit a clear understanding of the walls structural behavior, flow of internal forces and redistribution of stresses both in the pre- and post-peak regime.

Microprestress-Solidification Theory for Concrete Creep. I: Aging and Drying Effects

Abstract: A new physical theory and constitutive model for the effects of long-term aging and drying on concrete creep are proposed. The previously proposed solidification theory, in which the aging is explained and modeled by the volume growth (into the pores of hardened portland cement paste) of a nonaging viscoelastic constituent (cement gel), cannot explain long-term aging because the volume growth of the hydration products is too short-lived. The paper presents an improvement of the solidification theory in which the viscosity of the flow term of the compliance function is a function of a tensile microprestress carried by the bonds and bridges crossing the micropores (gel pores) in the hardened cement gel. The microprestress is generated by the disjoining pressure of the hindered adsorbed water in the micropores and by very large and highly localized volume changes caused by hydration or drying. The long-term creep, deviatoric as well as volumetric, is assumed to originate from viscous shear slips between the opposite walls of the micropores in which the bonds or bridges that cross the micropores and transmit the microprestress break and reform. The long-term aging exhibited by the flow term in the creep model is caused by relaxation of the tensile microprestress transverse to the slip plane. The Pickett effect (drying creep) is caused by changes of the microprestress balancing the changes in the disjoining pressure, which in turn are engendered by changes of the relative humidity in the capillary pores. Numerical implementation, application and comparison with test data is relegated to a companion paper that follows in this issue.

Effect of Length on Compressive Strain Softening of Concrete

Abstract: The concept of localization during the postpeak of compressive strain softening is presented. To explore localization in compression, a feedback-control method using a linear combination of displacement and force that partially subtracts the elastic response of the specimen to give a stable feedback signal is used. Results are presented from two test series (45 and 90 MPa) that use this method to test cylinders with length-to-diameter ratios ranging from 2.0 to 5.5 It is shown that compression failure is in fact a localized phenomenon. The compressive fracture energy is divided into energy dissipated in the prepeak and the postpeak portions of the stress-deformation response. It is found that the amount of energy required to propagate the compression failure during postpeak is independent of length for this range of specimens. The compressive fracture energies are compared for the normal and high-strength concretes.

Normal/Shear Cracking Model: Application to Discrete Crack Analysis

Abstract: A simple but general model for normal/shear cracking in quasi-brittle materials is presented. It is defined in terms of the normal and shear stresses on the average plane of the crack and the corresponding normal and shear relative displacements. A crack surface in stress space determines crack initiation under pure tension, shear-tension, or shear-compression loading. Two independent fracture energy parameters are used: the classical Mode I fracture energy GfI, and the asymptotic Mode II fracture energy GfIIa under very high shear-compression and no dilatancy. The cracking model proposed can be implemented in two ways: directly as the constitutive law of an interface element in the context of discrete crack analysis, or as the law of a generic cracking plane in a multicrack formulation in the context of smeared crack analysis. In this paper, the first approach is presented and examples are given of numerical constitutive testing and verification with experimental data.

Efficient reliability evaluation using spreadsheet

Abstract: A practical method using spreadsheets is proposed for calculating the Hasofer-Lind second moment reliability index 13. Two example problems involving correlated normals and correlated nonnormals, respectively, are solved and compared with established mathematical approach. The proposed method is based on the per­ spective of an ellipsoid that is tangent to the failure surface in the original space of the random variables; concepts of transformed space or reduced variates are not required. Correlation is accounted for by setting up the quadratic form in the spreadsheet. Nonnormals are dealt with using established relationships between non­ normal distribution and its equivalent normal distribution. Iterative searching is performed automatically by invoking a spreadsheet's optimization tool. An advantage of the spreadsheet method is that partial derivatives are not part of the input; the method may therefore be especially attractive for cases with complicated or nonexplicit performance functions.

Asymptotic Expansions for Reliability and Moments of Uncertain Systems

Abstract: An asymptotic approximation is developed for evaluating the probability integrals that arise in the determination of the reliability and response moments of uncertain dynamic systems subject to stochastic excitation. The method is applicable when the probabilities of failure or response moments conditional on the system parameters are available, and the effect of the uncertainty in the system parameters is to be investigated. In particular, a simple analytical formula for the probability of failure of the system is derived and compared to some existing approximations, including an asymptotic approximation based on second-order reliability methods. Simple analytical formulas are also derived for the sensitivity of the failure probability and response moments to variations in parameters of interest. Conditions for which the proposed asymptotic expansion is expected to be accurate are presented. Since numerical integration is only computationally feasible for investigating the accuracy of the proposed method for a small number of uncertain system parameters, simulation techniques are also used. A simple importance sampling method is shown to converge much more rapidly than straightforward Monte Carlo simulation. Simple structures subjected to white noise stochastic excitation are used to illustrate the accuracy of the proposed analytical approximation. Results from the computationally efficient perturbation method are also included for comparison. The results show that the asymptotic method gives acceptable approximations, even for systems with relatively large uncertainty, and in most cases, it outperforms the perturbation method.

Fully nonstationary analytical earthquake ground-motion model

Abstract: A versatile, nonstationary stochastic ground-motion model accounting for the time variation of both intensity and frequency content typical of real earthquake ground motions is formulated and validated. An extension of the Thomson's spectrum estimation method is used to adaptively estimate the evolutionary power spectral density (PSD) function of the target ground acceleration record. The parameters of this continuous-time, analytical, stochastic earthquake model are determined by least-square fitting the analytical evolutionary PSD function of the model to the target evolutionary PSD function estimated. As application examples, the proposed model is applied to two actual earthquake records. In each case, model validation is obtained by comparing the second-order statistics of several traditional ground-motion parameters and the probabilistic linear-elastic response spectra simulated using the earthquake model with their deterministic counterparts characterizing the target record.

Size effect in compression fracture: splitting crack band propagation

Abstract: A simplified fracture-mechanics-based model of compression failure of centrically or eccentrically loaded quasi-brittle columns is presented and the size effect on the nominal strength of a column is predicted. Failure is modeled as propagation of a band of axial splitting cracks in a direction orthogonal or inclined with respect to the column axis. The maximum load is calculated from the condition that the energy released from the column due to crack band advance be equal to the energy consumed by the splitting cracks. The axial stress transmitted across the crack band is determined as the critical stress for buckling of the microslabs of material between the axial splitting cracks, and the work on the microslabs during postbuckling deflections is taken into account. The critical postbuckling deflection of the microslabs is determined from a compatibility condition. Under the assumption of small enough material inhomogeneities, the spacing s of the splitting cracks is calculated by minimizing the failure load and is found to decrease with structure size D as D- 1/5 • The size effect on the nominal strength of geometrically similar columns is found to disappear asymptotically for small sizes D, and to asymptotically approach the power law D- 215 for large sizes D (where D = cross section dimension). However, when the material inhomogeneities are so large that they preclude the decrease of s with increasing D, the asymptotic size effect changes to D- '12 • The size effect intensifies with increasing slenderness of the column, which is explained by the fact that a more slender column stores more strain energy. The predicted size effect describes quite well previous tests at Northwestern University of reduced-scale tied reinforced concrete columns of different sizes (with size range 1:4) and different slenderness (ranging from 19 to 53). Finally, a simple modification is pointed out for the case of shear loading of concrete, in which a system of parallel tensile cracks in the diagonal compression direction develops before the maximum compressive stress is reached.

Damage detection and assessment of structures from static response

Abstract: A damage detection and assessment algorithm is developed based on a parameter estimation with an adaptive parameter grouping scheme. Damage is characterized by a reduction in a constitutive property of a parameterized finite-element model between two time-separated inferences. We assume that the baseline parameter values are known. An adaptive parameter grouping scheme is proposed to localize damage in a structural system for which the measured data are sparse. A data perturbation scheme is proposed both for the baseline structure, to establish the damage threshold above which damage can be confidently discerned from noise, and for the damaged structure, to compute the damage indices. To examine and illustrate the damage assessment algorithm, a numerical simulation study on a planar bowstring truss structure is performed.

Numerical Generation and Absorption of Fully Nonlinear Periodic Waves

Abstract: Permanent form periodic waves with zero-average mass flux are generated in a two-dimensional numerical wave tank solving fully nonlinear potential flow equations. An absorbing beach is modeled at the end of the tank in which (1) an external free-surface pressure absorbs energy from high frequency waves; and (2) a pistonlike condition absorbs energy from low-frequency waves. A feedback mechanism adaptively calibrates the beach parameters to absorb the period-averaged energy of incident waves. Wave generation and absorption are validated over constant depth, for tanks and beaches of various lengths, and optimal parameter values are identified for which reflection from the beach is reduced to a few percent. Shoaling of periodic waves is then modeled over a 1:50 slope, up to very close to the breaking point. A quasi-steady state is reached in the tank for which (not previously calculated) characteristics of fully nonlinear shoaling waves are obtained.

Microprestress-solidification theory for concrete creep. ii: algorithm and verification

Abstract: This paper presents a numerical algorithm for the microprestress-solidification theory developed in a companion paper and verifies this theory by comparisons with typical test data from the literature. A model for cracking is incorporated in the algorithm.

Micromechanical Simulation of Hot Mix Asphalt

Abstract: A model based on the discrete element method (DEM), ASBAL, was developed by modifying the TRUBAL program to simulate hot mix asphalt (HMA) To represent asphalt cement, several viscoelastic elements (ie, Maxwell, Kelvin-Voigt, and Burger's elements) were considered The research results from the Strategic Highway Research Program (SHRP) were used for the selection of proper element From these viscoelastic elements the Burger linear viscoelastic element is shown to be the most promising element for modeling asphalt binder behavior, based on mechanical responses and comparisons with physical experimental results Therefore, Burger's elements were added in normal and tangential directions to each aggregate-asphalt-aggregate contact to simulate the asphalt binder in HMA assemblies This new model is called ASBAL (TRUBAL for Asphalt) Several monotonic and cyclic tests were simulated to observe and fine-tune the model ASBAL A carefully conducted physical experiment with X-ray tomographs was simulated and c

System Identification with Limited Observations and without Input

Abstract: A time domain system identification technique is proposed to estimate the stiffness and damping parameters, at the element level, of a structure excited by unknown or unmeasured input forces. The unknown input forces could be of any type, including seismic loading. The unique feature of this technique is that it does not require response measurements at all dynamic degrees of freedom of the structure. This new procedure is a combination of an iterative least-squares procedure with unknown input excitations (ILS-UI) proposed earlier by the writers, and the extended Kalman filter method with a weighted global iteration (KF-WGI). The new procedure is denoted by the writers as ILS-EKF-UI. The uncertainty in the output responses is considered, and its effect on the accuracy of the identified parameters is analyzed. The efficiency, accuracy, and robustness of the proposed algorithm are illustrated by numerical examples. The accuracy of the proposed ILS-EKF-IU procedure is of the same order as that of ILS-UI; ho...

Semiactive control algorithms for structures with variable dampers

Abstract: Semiactive control systems combine the following features of active and passive control to reduce the response of structures to various dynamic loadings: (1) active variable stiffness, where the stiffness of the structure is adjusted to establish a nonresonant condition between the structure and excitation; and (2) active variable damper, where the damping coefficient of the device is varied to achieve the most reduction in the response This study is concerned with examining the effectiveness of variable dampers for seismic applications Three algorithms for selecting the damping coefficient of variable dampers are presented and compared They include a linear quadratic regulator algorithm; a generalized linear quadratic regulator algorithm with a penalty imposed on the acceleration response; and a displacement-acceleration domain algorithm, where the damping coefficient is selected by examining the response on the displacement-acceleration plane and assigning different damping coefficients accordingly Two single-degree-of-freedom structures subjected to 20 ground excitations are analyzed using the three algorithms The analyses indicate that, unlike passive dampers (where for flexible structures, an increase in damping coefficient decreases displacement but increases the acceleration response), variable dampers can be effective in reducing both the displacement and acceleration responses The algorithms are used to compute the seismic response of two structures: (1) an isolated bridge modeled as a single-degree-of-freedom system; and (2) a base-isolated six-story frame modeled as a multi-degree-of-freedom system The results indicate that variable dampers significantly reduce the displacement and acceleration responses

Random Vibration of Systems with Frequency-Dependent Parameters or Fractional Derivatives

Abstract: This technical note considers a class of models that describe dynamic systems with frequency-dependent parameters or fractional derivatives. These concepts are elucidated by introducing abstract state-space representations of dynamic systems or convolution integrals; the motion of these systems is governed by integrodifferential equations, and related Monte Carlo simulations can be conducted expeditiously. It is shown with mathematical rigor that the response of these systems to random excitation can be determined by a standard formula.

Fracture Parameters by Polylinear Tension-Softening Analysis

Abstract: Elastic-plastic fracture parameters for concrete were proposed based on the cohesive force model (CFM) and polylinear approximation analyses of the tension-softening diagram (TSD). The prediction method for the load-displacement relationships of concrete with cracks was developed by means of the fictitious crack model concept with the K-superposition method and the constitutive law of the polylinear TSD. In this method the nonlinear crack equation was solved by an iteration program for evaluating the optimum softening inclinations of TSD. The polylinear approximation method for calculating the complete TSD from the actual load-displacement curve was established by using the stepped inverse analysis. The energy consumed by fracturing (dWf) was calculated by integrating the work done by a cohesive force acting on the fictitious crack surface. Fracture parameters for elastic-plastic materials such as Gp, which is the energy release rate of CFM, R-curve, and fracture energy were estimated based on the value o...

BRITTLE FRACTURE IN PLANE ELEMENTS WITH SHARP NOTCHES UNDER MIXED-MoDE LOADING

Abstract: Plane structural elements with sharp wedge-shaped notches are considered and the conditions for crack initiation are discussed The use of the Griffith energy condition would require the assumption of pre-existence of a plane crack emanating from the notch vertex at specified direction To avoid this assumption, a nonlocal crack initiation and propagation condition proposed by Seweryn and Mroz is applied to study crack initiation This condition is expressed in terms of normal and tangential traction components acting on a physical plane segment of specified dimension Mixed-mode conditions are considered for which both critical load value and crack orientation are predicted The generalized stress intensity factors at the notch tip are determined by applying finite elements accounting for stress singularity A special device was constructed in order to generate mixed-mode loading conditions in a tensile machine The experimental program was executed in order to verify predictions of critical load variati

Causal Hysteretic Element

Abstract: In this paper the “\Icausal hysteretic element\N”is constructed and analyzed. The dynamic stiffness of the proposed hysteretic model has the same imaginary part as the “ideal” hysteretic damper, but has the appropriate real part that makes the model causal. The proposed model is constructed by requiring that the real and imaginary parts of its transfer functions satisfy the Kramers-Kroning relations. This condition ensures that the corresponding time response functions of the proposed model are zero at negative times. The causal hysteretic element is physically realizable at finite frequencies, but at ω = 0 is not definable. The behavior of the proposed model is analyzed both in frequency and time domain. It is shown that the causal hysteretic element is the limiting case of a linear viscoelastic model with nearly frequency-independent dissipation. Finally, the response of a mass supported by the causal hysteretic element is discussed.

Response of elastic continuum carrying moving linear oscillator

Abstract: This paper presents a method for solving the problem of the dynamic response of a continuous elastic structure carrying a moving linear oscillator. The method reduces the problem to the integration of a system of linear ordinary differential equations governing the time-dependent coefficients of the series expansion of the response in terms of the eigenfunctions of the continuous structure. The method is simple and elegant and can be applied to any conservative spatially one-dimensional continuum with arbitrary boundary conditions.

Localizing a Notch in a Steel Frame from Frequency Measurements

Abstract: Most of the diagnostic techniques via modal analysis are based on an optimality criterion where the stiffness distribution of a chosen reference configuration of the structural system is updated so that the first few natural frequencies closely match the measured ones at a certain level of deterioration. Despite the common use of these techniques in damage identification, basic questions such as how accurate the reference configuration has to be or which \Ia priori\N hypotheses are needed to get around the badly posed diagnostic problem are unclear and still open. In this paper a diagnostic strategy for identifying a localized damage in a multistory steel frame is discussed, with an eye to these questions and to practical use of vibration monitoring on field measurements. It was found that the dynamic characterization of the frame at a certain stage of its service is indispensable to defining an accurate analytical model of the structure, that is, to defining a reference configuration of the frame that is useful for identifying possible incremental damages. Moreover, some working hypotheses commonly used in structural diagnostics were found to be crucial in reducing the indeterminacy of the identification problem. The obtained results essentially confirm a more careful resolution on the localization of the damage as its severeness increases.

Viscoelastic Analysis of Diametral Compression of Asphalt Concrete

Abstract: The diametral compression of short cylinders is generally accepted as the convenient and accurate test method for evaluating the mechanical properties of asphalt concrete mixtures. In particular, the test serves to determine the relation between the stresses and strains, with the assumption that it can be quantified by the elastic (resilient) modulus and Poisson's ratio. These parameters are used for both the asphalt concrete quality assessment and in elastic multilayer analytic or numerical predictions of pavement deflections. The elasticity-based test analysis used in practice accounts for viscous effects that asphalt concrete displays at moderate and elevated temperatures in a simplified fashion. The methodology presented in this paper incorporates the effect of viscosity in a rigorous manner, by deriving a linear viscoelasticity-based solution. The solution makes use of the elastic-viscoelastic correspondence principle and Laplace and Fourier transforms; it is valid for any load history. Specifically,...

Acoustic Emission Source Location Using Lamb Wave Modes

Abstract: This paper describes the development of a technique based on acoustic emission (AE) technology that can be used for global nondestructive evaluation (NDE) of steel structures. This will also be useful for the subsequent local inspection used to further monitor cracking, defective connections, retrofit measures, and so forth. The dispersive nature of Lamb wave propagation in plates makes it possible to perform a linear source location of AE events based on the arrival of different frequency components (Lamb wave modes) of an AE event at a single transducer. Experiments on steel beams and plates in the laboratory explored the theory of wave propagation and digital signal processing needed to pursue this objective. Subsequent field investigation on a real bridge substantiated the applicability of this technique. This new technique could allow AE inspection to locate structural problems better, and with a reduced number of transducers.

Crack Growth and Lifetime of Concrete under Long Time Loading

Abstract: Edge-notched eccentrically compressed fracture specimens made of aggregate of reduced size are loaded in standard creep test frames. Measurements of the time rate of crack mouth opening in notched concrete specimens subjected to constant load of almost one month duration are reported and analyzed. To reveal the size effect, geometrically similar specimens of four sizes in the ratio I :2:4:8 are tested. The results are success­ fully described by a previously proposed time-dependent generalization of the R-curve model, in which the rate of crack growth is a function of the ratio of the stress intensity factor to the R-curve, and linear aging viscoelastic creep in the bulk of the specimen is treated according to the operator method. Good predictions are also obtained with a simplified method in which the R-curve is replaced by a constant asymptotic value of the critical stress intensity factor and creep is handled in similarity to the effective modulus method, neglecting the history effect. The time curves of crack opening terminate with an infinite slope, indicating the lifetime. The finiteness of the lifetime is not caused by creep, but by time-dependent crack growth, which dominates the final stage of crack opening. The initial stage of crack opening, on the other hand, is dominated by creep. Tests are conducted both for concretes of normal strength of 33.4 MPa (4,847 psi) in compression and relatively high strength of 46.4 MPa (6,442 psi). For the stronger concrete, the lifetimes are found to be longer. An increase of specimen size is found to decrease the lifetime. Since the same type of model was previously shown capable of describing all other known time-dependent fracture phenomena in concrete, a rather general applicability may be expected.

Ritz Method for Vibration Analysis of Cylindrical Shells with Ring Stiffeners

Abstract: It is generally perceived that it is awkward to automate the Ritz method for structural analysis because the Ritz functions that satisfy one combination of boundary conditions cannot be used for another To handle general boundary conditions, analysts thus resort to the use of Lagrangian multipliers or discretization methods such as the finite-element method, finite-difference method, and the differential quadrature method Contrary to the foregoing perception, this paper demonstrates the manner in which the Ritz method can be conveniently automated for the vibration analysis of cylindrical shells with varying ring-stiffener distribution To achieve this, a set of Ritz functions is proposed that contains the boundary equations raised to appropriate integer powers so that the geometric boundary conditions are satisfied a priori The presented Ritz formulation has been nondimensionalized to obtain generic solutions for shells with various stiffener distributions Based on these solutions, the effects of stiffener eccentricity, number, sizes, and locations on the vibration frequencies were examined

EVOLUTIONARY MODEL OF VISCOELASTIC DAMPERS FOR STRUCTURAL ApPLICATIONS

Abstract: Th 7 effe~ts oftempe~atureon the energy dissipation of viscoelastic dampers for seismic mitigation of structures are mvestigated. To Simulate the damper behavior, an evolutionary model is proposed to describe ~e dependence o~ ~e ~echanical propertie~ of th~ damper on the deformation frequency and the temperature mcre~e due to diSSipation. Thermorheologlcally Simple materials are considered and the influence of the de­ formatio~ frequency on the storage and loss moduli is modeled using fractional derivative operators. The effect of m~tenal temperature on the for~e-~eformation relation is modeled using the concept of evolutionary transfer func~0!1' and the proposed model IS Implemented using a step-by-step technique in the frequency domain. The p~edictions. of the proposed. model in the case of sinusoidal and seismic deformations show good agreement with e~penmental results. Fmally, the response spectra of single-degree-of-freedom structures with added vis­ coelastic ~pers and subjected to seismic excitation are computed using the proposed evolutionary model; the results obtained show that the thermal effect due to energy dissipation is not always negligible.

Fracturing truss model: size effect in shear failure of reinforced concrete

Abstract: The classical truss model (or strut-and-tie model) for shear failure of reinforced concrete beans is modified to describe fracture phenomena during failure. The failure is assumed to be caused by propagation of a compression fracture across the concrete strut during the portion of the loading history in which the maximum load is reached. The compression fracture may consist of a band of splitting cracks that later interconnect to form a shear crack or a shear fracture band inclined to the strut. The width of the fracture band is assumed to occupy only a portion of the strut length and to represent a fixed material property independent of the beam depth. The energy release from the truss is calculated using two alternative approximate methods: (1) using the potential energy change deduced from the concept of stress relief zones; and (2) using the complementary energy change due to stress redistribution caused by propagation of the fracture band across the compressed concrete strut. Both approaches show that a size effect on the nominal strength of shear failure must exist and that it should approximately follow the size effect law proposed by Bazant in 1984. The physical mechanism of the size effect is also explained in a clear and simple intuitive manner. Finally, it is shown that the applied nominal shear stress that causes large initial diagonal cracks to form also exhibits a size effect.

Bending Analysis of Simply Supported Shear Deformable Skew Plates

Abstract: This paper presents the bending analysis of a simply supported, thick skew plate based on the first-order shear deformation Reissner/Mindlin theory. Using the geometric transformation, the governing differential equations and boundary conditions of the plate are first transformed from the physical domain into a unit square computational domain. A set of linear algebraic equations is then derived from the transformed differential equations via a numerical technique, the differential quadrature method (DQM), and the approximate solutions of the problem are obtained by solving the set of algebraic equations. The applicability, accuracy, and convergent properties of DQM for the bending analysis of simply supported skew plates are carefully examined for various skew angles and various relative plate thickness. In this paper, the central deflections and moments of the plate are presented for different thickness-to-span ratios, and skew angles for future references.

Using Modal Analysis for Estimation of Anisotropic Material Constants

Abstract: A dynamic method is presented for the estimation of the in-plane elastic properties of structural panels modeled as thin orthotropic plates. The method utilizes the concept of modal analysis. Results from experimental modal testing are matched with theoretical modal analysis calculations for a set of plate bending modes and one in-plane mode of the compression type. The elastic constants \iE\d1, \iE\d2, and \iG\d1\d2 are estimated by minimizing the relative errors between corresponding experimentally and theoretically determined eigenfrequencies. A ratio of two chosen mode shape values of an in-plane compression mode yields an estimate of the Poisson ratio ν\d2\d1. The other in-plane Poisson’s ratio ν\d1\d2 is calculated on the basis of \iE\d1, \iE\d2, and ν\d2\d1 using Hooke’s generalized law. Some redundant information gained from the experimental modal testing is used to minimize possible errors in the test and evaluation process. The method is applied to one type of wood panel material, namely oriented strand board.