Second-Order Sensitivities of Inelastic Finite-Element Response by Direct Differentiation

In this paper analytical equations are developed and implemented to obtain second-order derivatives of finite-element responses with respect to input parameters. The work extends previous work on first-order response sensitivity analysis. Of particular interest in this study is the computational feasibility of obtaining second-order response sensitivities. In the past, the straightforward finite difference approach has been available, but this approach suffers from serious efficiency and accuracy concerns. In this study it is demonstrated that analytical differentiation of the response algorithm and subsequent implementation on the computer provides second-order sensitivities at a significantly reduced cost. The sensitivity results are consistent with and have the same numerical precision as the ordinary response. The computational cost advantage of the direct differentiation approach increases as the problem size increases. Several novel implementation techniques are developed in this paper to optimize the computational efficiency. The derivations and implementations are demonstrated and verified with two finite-element analysis examples.     

Handling of Constraints in Finite-Element Response Sensitivity Analysis

In this paper, the direct differentiation method (DDM) for finite-element (FE) response sensitivity analysis is extended to linear and nonlinear FE models with multi-point constraints (MPCs). The analytical developments are provided for three different constraint handling methods, namely: (1) the transformation equation method; (2) the Lagrange multiplier method; and (3) the penalty function method. Two nonlinear benchmark applications are presented: (1) a two-dimensional soil-foundation-structure interaction system and (2) a three-dimensional, one-bay by one-bay, three-story reinforced concrete building with floor slabs modeled as rigid diaphragms, both subjected to seismic excitation. Time histories of response parameters and their sensitivities to material constitutive parameters are computed and discussed, with emphasis on the relative importance of these parameters in affecting the structural response. The DDM-based response sensitivity results are compared with corresponding forward finite difference analysis results, thus validating the formulation presented and its computer implementation. The developments presented in this paper close an important gap between FE response-only analysis and FE response sensitivity analysis through the DDM, extending the latter to applications requiring response sensitivities of FE models with MPCs. These applications include structural optimization, structural reliability analysis, and finite-element model updating.     

Dimensional Analysis of Rigid-Plastic and Elastoplastic Structures under Pulse-Type Excitations

In this paper, the inelastic response of rigid-plastic and elastic-plastic systems subjected to pulse-type excitations is revisited with dimensional analysis. Starting from Newmark’s result on the maximum displacement of a sliding mass resting on a base that is subjected to a rectangular acceleration pulse, the paper introduces an energetic length scale of the excitation and the relevant dimensionless Π-products that govern the response of yielding structures. The introduction of Buckingham’s Π-theorem reduces the number of variables that govern the response of the elastic-plastic system from five (5) to three (3). The proposed dimensionless Π-products are liberated from the associated elastic system response and are consistent with the incremental evolution from the rigid-plastic to the elastic-plastic system. When the response is presented in terms of the dimensionless Π-terms remarkable order emerges. It is shown that for a given value of dimensionless yield displacement the response curves (maximum relative dimensionless displacements) become self-similar and follow a single master curve. The self-similar solutions show clearly how the inelastic response amplifies as the normalized yield displacement increases and that an increase in strength may lead to an increase in inelastic displacements. The main advantage of the analysis presented in this paper is that it brings forward the concept of self-similarity—an invariance with respect to changes in scale or size—which is a decisive symmetry that shapes nonlinear behavior.     

Dimensional Analysis of the Earthquake Response of a Pounding Oscillator

In this paper, the dynamic response of a pounding oscillator subjected to pulse type excitations is revisited with dimensional analysis. The study adopts the concept of the energetic length scale which is a measure of the persistence of the distinguishable pulse of strong ground motions and subsequently presents the dimensionless Π products that govern the response of the pounding oscillator. The introduction of Buckingham’s Π theorem reduces the number of variables that govern the response of the system from 7 to 5. The proposed dimensionless Π products are liberated from the response of an oscillator without impact and most importantly reveal remarkable order in the response. It is shown that, regardless the acceleration level and duration of the pulse, all response spectra become self-similar and, when expressed in the dimensionless Π products, follow a single master curve. This is true despite the realization of contacts with increasing durations as the excitation level increases. All physically realizable contacts (impacts, continuous contacts, and detachment) are captured via a linear complementarity approach. The proposed analysis stresses the appreciable differences in the response due to the directivity of the excitation (toward or away the stationary wall) and confirms the existence of three spectral regions where the response of the pounding oscillator amplifies, deamplifies, and equals the response of the oscillator without pounding.     

Establishing a limit of recognition for a vapor sensor array

Organic vapor analysis with microsensor arrays relies principally on two output parameters: the response pattern, which provides qualitative information, and the response sensitivity, which determines the limit of detection (LOD). The latter is used to define the operating limit in the low-concentration range, under the implicit assumption that, if a vapor can be detected, it can be identified and differentiated from other vapors on the basis of its response pattern. In this study, the performance of an array of four polymer-coated surface acoustic wave vapor sensors was explored using calibrated response data from 16 solvent vapors in Monte Carlo simulations coupled with pattern recognition analysis. The statistical modeling revealed that the ability to recognize a vapor from its response pattern decreases with decreasing vapor concentration, as expected, but also that the concentration at which errors in vapor recognition become excessive is well above the calculated LOD in most cases, despite the LOD being based on the least sensitive sensor in the array. These results suggest the adoption of a limit of recognition (LOR), defined as the concentration below which a vapor can no longer be reliably recognized from its response pattern, as an additional criterion for evaluating the performance of multisensor arrays. A generalized method for estimating the LOR is presented, as well as a means for improving the LOR via residual error analysis.     

Quasi-Static Response of Fixed Offshore Platforms to Morison-Type Wave Loadings

The stochastic response of a rigid platform is quasi-static and can be represented as a linear combination of nonlinear random wave loadings. In this study two efficient probabilistic approaches are respectively presented to estimate the higher-order statistics of mildly and highly non-Gaussian structural responses. The eigenvalue analysis of structural quasi-static response in the first approach is based on the expansion of the response in terms of independent Gaussian random variables. The second approach extends the earlier quasi-static analysis procedures to obtain the higher moments of response by including current effects and inundation effects. The interested prediction of extreme responses during a short-term storm, by mean upcrossing rates and mean extremes, can then be achieved by applying Winterstein’s functional transformation. These quantities are found in good agreement with not only Monte Carlo simulation results but also the extreme values obtained using a recently proposed method by Naess et al. in 2007.     

Red light-induced appearance of phosphotyrosine-like epitopes on nuclear proteins from pea (Pisum sativum L.) plumules

As assayed by western blot analysis, red light induces the appearance of epitopes recognized by anti-phosphotyrosine antibodies in several pea nuclear proteins. The immunostaining is blocked by preadsorbing the antibodies with phosphotyrosine but not by preadsorbing them with phosphoserine or phosphothreonine. This light response is observed whether the red light irradiation is given to pea plumules or nuclei isolated from the plumules. The red-light-induced response seen in plumules is reversible by a subsequent far-red-light irradiation, indicating that the likely photoreceptor for this response may be phytochrome. By immunoblot analysis pea phytochrome A, but not phytochrome B, can be detected in proteins extracted from pea nuclear chromatin-matrix preparations. Phytochrome A and the protein bands immunostained by anti-phosphotyrosine antibodies can be solubilized from unirradiated pea chromatin by 0.3 M NaCl, but irradiating this preparation with red light does not induce the appearance of phosphotyrosine-like epitopes in any nuclear proteins. These results suggest that the association of phytochrome with purified pea nuclei is such that its conversion to the far-red light-absorbing form can induce a post-translational epitope change in nuclear proteins in vivo.     

Aeroelastic Analysis of Bridges: Effects of Turbulence and Aerodynamic Nonlinearities

Current linear aeroelastic analysis approaches are not suited for capturing the emerging concerns in bridge aerodynamics introduced by aerodynamic nonlinearities and turbulence effects. These issues may become critical for bridges with increasing spans and/or with aerodynamic characteristics sensitive to the effective angle of incidence. This paper presents a nonlinear aerodynamic force model and associated time domain analysis framework for predicting the aeroelastic response of bridges under turbulent winds. The nonlinear force model separates the aerodynamic force into low- and high-frequency components according to the effective angle of incidence. The low-frequency force component is modeled utilizing quasi-steady theory. The high-frequency force component is based on the frequency dependent unsteady aerodynamic characteristics, which are similar to the traditional force model but vary in space and time following the low-frequency effective angle of incidence. The proposed framework provides an effective analysis tool to study the influence of structural and aerodynamic nonlinearities and turbulence on the bridge aeroelastic response. The effectiveness of this approach is demonstrated by utilizing an example of a long span suspension bridge with aerodynamic characteristics sensitive to the angle of incidence. The influence of mean wind angle of incidence on the aeroelastic modal properties and the associated aeroelastic response and the sensitivity of bridge response to nonlinear aerodynamics and low-frequency turbulence are examined.     

Nonlinear Response Analysis Considering Dynamic Stiffness with Both Frequency and Strain Dependencies

The time domain evaluation of the frequency-dependent dynamic stiffness was studied and some transform methods are being proposed. In this paper, the nonlinear response analysis method of the dynamic stiffness with both frequency and strain dependency was studied. First, the frequency-dependent complex stiffness was calculated at each strain level, and then they were transformed to the impulse response in the time domain. The characteristics of the complex stiffness and the impulse response of both two-layered soil and viscoelastic dampers were investigated. Then, the nonlinear time-history response analysis method considering both dependencies using the impulse response of each strain level was proposed. The earthquake response analysis of a structure on the two-layered soil was carried out as an example. The efficiency of the method was confirmed through these investigations.     

Effect of Asynchronous Earthquake Motion on Complex Bridges. II: Results and Implications on Assessment

Nonuniform seismic excitation has been shown through previous analytical studies to adversely affect the response of long-span bridge structures. To further understand this phenomenon, this study investigates the response of complex straight and curved long-span bridges under the effect of parametrically varying asynchronous motion. The generation process and modeling procedures are presented in a companion paper. A wide-ranging parametric study is performed aimed at isolating the effect of both bridge curvature and the two main sources of asynchronous strong motion: geometric incoherence and the wave-passage effect. Results from this study indicate that response for the 344?m study structure is amplified significantly by nonsynchronous excitation, with displacement amplification factors between 1.6 and 3.4 for all levels of incoherence. This amplification was not constant or easily predicable, demonstrating the importance of inelastic dynamic analysis using asynchronous motion for assessment and design of this class of structure. Additionally, deck stiffness is shown to significantly affect response amplification, through response comparison between the curved and an equivalent straight bridge. Study results are used to suggest an appropriate domain for consideration of asynchronous excitation, as well as an efficient methodology for analysis.     

Aeroelastic Analysis of Bridges under Multicorrelated Winds: Integrated State-Space Approach

In this paper, an integrated state-space model of a system with a vector-valued white noise input is presented to describe the dynamic response of bridges under the action of multicorrelated winds. Such a unified model has not been developed before due to a number of innate modeling difficulties. The integrated state-space model is realized based on the state-space models of multicorrelated wind fluctuations, unsteady buffeting and self-excited aerodynamic forces, and the bridge dynamics. Both the equations of motion at the full order in the physical coordinates and at the reduced-order in the generalized modal coordinates are presented. This state-space model allows direct evaluation of the covariance matrix of the response using the Lyapunov equation, which presents higher computational efficiency than the conventional spectral analysis approach. This state-space model also adds time domain simulation of multicorrelated wind fluctuations, the associated unsteady frequency dependent aerodynamic forces, and the attendant motions of the structure. The structural and aerodynamic coupling effects among structural modes can be easily included in the analysis. The model also facilitates consideration of various nonlinearities of both structural and aerodynamic origins in the response analysis. An application of this approach to a long-span cable-stayed bridge illustrates the effectiveness of this scheme for a linear problem. An extension of the proposed analysis framework to include structural and aerodynamic nonlinearities is immediate once the nonlinear structural and aerodynamic characteristics of the bridge are established.     

Use of multivariate analysis in medical chemistry]

If the repeated presentation of a single (standard) auditory stimulus is randomly interspersed with a second acoustically different (deviant) stimulus, the cortical activity evoked by the deviant stimulus can contain a negative component known as the mismatch negativity (MMN). The MMN is derived by subtracting the averaged response evoked by the standard stimulus from that evoked by the deviant stimulus. When the magnitude of the response is small or the signal-to-noise ratio is poor, it is difficult to judge the presence or absence of the MMN simply by visual inspection, and statistical detection techniques become necessary. A method of analysis is proposed to quantify the magnitude and statistically evaluate the presence of the MMN based on time-integrated evoked responses. This paper demonstrates the use of this integrated mismatch negativity (MMNi) analysis to detect the MMN evoked by stimulus contrasts near the perceptual threshold of two subjects. The MMNi, by virtue of being equivalent to a low-pass filtered response, presents an almost noise-free estimate of MMN magnitude. A single measure of the integrated evoked response at a fixed time point is used in a distribution-free statistic that compares the magnitude of the averaged response evoked by the deviant stimulus with a magnitude distribution derived from 200 subaveraged responses to the standard stimulus (with the number of sweeps per average equal to that of the deviant stimulus). This allows a calculation of the exact probability for the null hypothesis that the negative magnitude of the response evoked by the deviant stimulus is drawn from the magnitude distribution of responses evoked by the standard stimulus. Rejection of this hypothesis provides objective evidence of the presence of the MMN.     

New Approach for Seismic Nonlinear Analysis of Inelastic Framed Structures

A novel approach for seismic nonlinear analysis of inelastic framed structures is presented in this paper. The nonlinear analysis refers to the evaluation of structural response considering P-delta effect, which is in the form of geometric nonlinearity, and inelastic behavior refers to material nonlinearity. This novel approach uses finite element formulation to derive the elemental stiffness matrices, particularly to derive the geometric stiffness matrix in a general form. At the same time, this approach separates the inelastic displacement from total deflection of the structure by applying two additional constant matrices, namely, the force–recovery matrix and the moment-restoring matrix in the force analogy method. The benefit behind this treatment is explicitly locating and calculating the inelastic response, together with strategically separating the coupling effect between the material nonlinearity and geometric nonlinearity, during the time history analysis. Comparison with the traditional incremental methods shows that the proposed method is very time efficient as well as straightforward. One portal frame and one five-story frame are used as numerical examples to illustrate and verify the robustness of current approach.     

Liquefaction and Deformation Analyses Using a Total Stress Approach

Estimating deformations due to seismically induced liquefaction is often accomplished with a series of simplified uncoupled analyses. An alternative approach is presented in this paper that builds upon this common practice while making significant improvements to the modeling quality. A two-dimensional finite-difference analysis is performed in the time domain using a simple plasticity-based constitutive model. The triggering of liquefaction is assessed in each element by continuously weighting the cyclic shear stress history. Liquefaction is initially predicted in the most susceptible elements and then progressively spreads as the earthquake continues. The properties of liquefied elements are adjusted at the instant of liquefaction to reflect the anticipated loss of strength and stiffness. Dynamic equilibrium is always maintained so that computed deformations are rationally affected by the structural response, progressing liquefaction, and gravity forces. The method is demonstrated through application to the Upper San Fernando Dam and its response to the San Fernando earthquake of 1971. The objective of this approach is to achieve a practical balance between a rigorous numerical and theoretical analysis and currently accepted practice.     

Simulated Micromechanical Models Using Artificial Neural Networks

A new method, termed simulated micromechanical models using artificial neural networks (MMANN), is proposed to generate micromechanical material models for nonlinear and damage behavior of heterogeneous materials. Artificial neural networks (ANN) are trained with results from detailed nonlinear finite-element (FE) analyses of a repeating unit cell (UC), with and without induced damage, e.g., voids or cracks between the fiber and matrix phases. The FE simulations are used to form the effective stress-strain response for a unit cell with different geometry and damage parameters. The FE analyses are performed for a relatively small number of applied strain paths and damage parameters. It is shown that MMANN material models of this type exhibit many interesting features, including different tension and compression response, that are usually difficult to model by conventional micromechanical approaches. MMANN material models can be easily applied in a displacement-based FE for nonlinear analysis of composite structures. Application examples are shown where micromodels are generated to represent the homogenized nonlinear multiaxial response of a unidirectional composite with and without damage. In the case of analysis with damage growth, thermodynamics with irreversible processes (TIP) is used to derive the response of an equivalent homogenized damage medium with evolution equations for damage. The proposed damage formulation incorporates the generalizations generated by the MMANN method for stresses and other possible responses from analysis results of unit cells with fixed levels of damage.     

Measuring needs with the Thematic Apperception Test: A psychometric study.

Three apperception theories that explain how people respond to Thematic Apperception Test cards are proposed: a simple apperception theory, an apperception theory with a dynamic component, and an apperception theory with 2 types of responses. Each theory is translated into an item response theory model and is applied to need for achievement (nAch) data. The analysis indicates that the best fitting model is provided by the apperception theory with 2 types of responses, also referred to as the drop-out apperception theory. The 1st type of response predicted by this theory is determined by the nAch level of the person and the achievement-response-eliciting value of the card; this response is diagnostic for the nAch level of the person. The 2nd type of response is not determined by the 2 aforementioned characteristics and is therefore not diagnostic of the person's nAch level. The results are cross-validated for need for power and need for affiliation. (PsycINFO Database Record (c) 2010 APA, all rights reserved)     

Influence of Input Motion and Site Property Variabilities on Seismic Site Response Analysis

Seismic site response analysis evaluates the influence of local soil conditions on earthquake ground shaking. There are multiple sources of potential uncertainty in this analysis; the most significant pertaining to the specification of the input motions and to the characterization of the soil properties. The influence of the selection of input ground motions on equivalent-linear site response analysis is evaluated through analyses performed with multiple suites of input motions selected to fit the same target acceleration response spectrum. The results indicate that a stable median surface response spectrum (i.e., within ±20% of any other suite) can be obtained with as few as five motions, if the motions fit the input target spectrum well. The stability of the median is improved to ±5 to 10% when 10 or 20 input motions are used. If the standard deviation of the surface response spectra is required, at least 10 motions (and preferably 20) are required to adequately model the standard deviation. The influence of soil characterization uncertainty is assessed through Monte Carlo simulations, where variations in the shear-wave velocity profile and nonlinear soil properties are considered. Modeling shear-wave velocity variability generally reduces the predicted median surface motions and amplification factors, most significantly at periods less than the site period. Modeling the variability in nonlinear properties has a similar, although slightly smaller, effect. Finally, including the variability in soil properties significantly increases the standard deviation of the amplification factors but has a lesser effect on the standard deviation of the surface motions.     

Seismic Earth Pressure on Retaining Structures

A simple kinematic method to predict the seismic earth pressure against retaining structures is developed. The fundamental solution to the free-field seismic response considering nonlinear, plastic behavior of soil is included in the retaining wall analysis for the first time. Perturbation to the free-field response caused by soil-structure interaction effects for different types of wall movement is considered. Results from this kinematic method are compared with those obtained from finite-element analysis and observed from laboratory shaking table tests performed on model retaining walls.     

Analysis of Scaling and Instability in FRP-Concrete Shear Debonding for Beam-Strengthening Applications

The debonding mode of failure, which is observed in girders strengthened using externally attached fiber-reinforced polymer (FRP) sheets, is studied in this paper. A numerical analysis of the direct-shear response of FRP attached to concrete substrate is performed to study the initiation, formation, and propagation of an interfacial crack between the two adherents. The material response of the bimaterial interface, which includes postpeak softening, is incorporated into the numerical model. The load response obtained numerically is shown to be in close agreement with that determined experimentally from direct shear tests on concrete blocks strengthened with FRP sheets. An instability in the load response is predicted close to failure and the arc-length method is used to obtain the entire load response past the displacement-limit point. The instability in the load response is shown to be a result of snapback, where both the load and the displacement decrease simultaneously. The effect of the bonded length on the stress transfer between the FRP and concrete and on the ultimate failure is also analyzed. It is shown that there is a scaling in the load capacity when the bonded length does not allow for the establishment of the full stress-transfer zone associated with interface crack growth. From the results of the numerical analysis, a fundamental understanding of interfacial crack propagation and instability at failure in concrete members strengthened using externally bonded FRP is developed. Using a simple energy based formulation; it is shown that in strengthened girders, the instability at complete debonding of FRP from concrete translates into an explosive failure associated with a sudden release of energy.