Nonlinear Analysis Procedure Research Articles

Rehabilitation of a 1985 Steel Moment-Frame Building

A 1985 steel moment frame is seismically upgraded using passive energy dissipation, without adding stiffness to the system. The design and analysis techniques for sizing the Velocity Braces™ and their impact on the demand capacity ratios are reviewed. The structure was built in the San Francisco Bay Area in compliance with the 1985 Uniform Building Code (UBC). The moment frame contains the classic pre-Northridge nonductile moment connection, complete with weld backup bars left attached. Nonlinear time-history analysis procedures were implemented to verify the demand capacity ratios at the critical beam-column connections. Flexural demand capacity ratios of .6 achieve elastic behavior in the design basis earthquake with R=1.0. The response spectra of the time history chosen for design exceed the requirements of the 1997 UBC Zone 4. Torsional response to earthquake excitation is minimized by strategic placement of nonlinear viscous dampers. Nonlinear dampers that reduce the flexural demand on joints and control interstory drift without inelastic excursions of the beam flanges are achieved. Floor spectral accelerations and maximum drift limits are reduced to be consistent with immediate occupancy performance. The damper driver mechanism, being velocity driven, reduces moment frame demands and allows flexibility in configuration.

NON-STATIONARY DYNAMICS DATA ANALYSIS WITH WAVELET-SVD FILTERING

Non-stationary time–frequency analysis is used for identification and classification of aeroelastic and aeroservoelastic dynamics. Time–frequency multiscale wavelet processing generates discrete energy density distributions. The distributions are processed using the singular-value decomposition (SVD). Discrete density functions derived from the SVD generate moments that detect the principal features in the data. The SVD standard basis vectors are applied and then compared with a transformed-SVD, or TSVD, which reduces the number of features into more compact energy density concentrations. Finally, from the feature extraction, wavelet-based modal parameter estimation is applied. The primary objective is the automation of time–frequency analysis with modal system identification. The contribution is a more general approach in which distinct analysis tools are merged into a unified procedure for linear and non-linear data analysis. This method is first applied to aeroelastic pitch-plunge wing section models. Instability is detected in the linear system, and non-linear dynamics are observed from the time-frequency map and parameter estimates of the non-linear system. Aeroelastic and aeroservoelastic flight data from the drone for aerodynamic and structural testing and F18 aircraft are also investigated and comparisons made between the SVD and TSVD results. Input–output data are used to show that this process is an efficient and reliable tool for automated on-line analysis. Published by Elsevier Science Ltd.

Earthquake response of tall reinforced concrete chimneys

The results from an experimental program have been used to develop a non-linear dynamic analysis procedure for evaluating the inelastic response of tall reinforced concrete chimney structures. The procedure is used to study the inelastic response of ten chimneys, ranging in height from 115 m to 301 m subject to earthquake excitation. Based on the study, a series of code design recommendations have been prepared and incorporated into the 2001 CICIND code to encourage reliance on the development of ductility in reinforced concrete chimneys and to prevent the formation of brittle failure modes. The basis for the selection of a structural response factor of R=2 which halves the seismic design forces is presented. The design recommendations result in both improved performance and cost savings of up to 20% compared with designs undertaken with the 1998 ACI307 and 1998 CICIND codes.

Nonlinear Pressurization and Modal Analysis Procedure for Dynamic Modeling of Inflatable Structures

Covers advancements in spacecraft and tactical and strategic missile systems, including subsystem design and application, mission design and analysis, materials and structures, developments in space sciences, space processing and manufacturing, space operations, and applications of space technologies to other fields.

Contribution of Nonlinear Finite-Element Analysis to Evaluation of Two Structural Concrete Failures

The failure of two reinforced concrete structures is recounted, one involving a warehouse structure and the other an offshore platform base structure. Design details and factors leading to the collapses are identified and discussed. The structures were subsequently analyzed using nonlinear finite-element analysis procedures, taking into account relevant second-order behavior models. The analyses provided an accurate assessment of the load capacities and failure modes observed, as well as meaningful insights into the underlying behavior mechanisms and factors leading to the failures. This paper supports the view that nonlinear analysis techniques have become useful everyday tools for design office applications, particularly in forensic work, and also gives evidence suggesting that errors in the design of modern structures can be potentially more catastrophic than in the past, and that advanced assessment techniques will assume increased importance as a result.

A parallel procedure for nonlinear analysis of reinforced concrete three-dimensional frames

The paper discusses the parallelisation of complex three-dimensional software for nonlinear analysis of R/C buildings structures. It presents a comparative study for handling the nonlinear response in different parallel architectures. The nonlinear finite element model adopts a fiber decomposition approach for the cross-section of beam elements to capture nonlinear behavior of concrete. The parallelisation strategy is designed regarding three items: the numerical stability of the nonlinear procedure, the parallel sparse equation solver and the application on heterogeneous hardware: dedicated shared memory machines or clusters of networked personal computers.

철근콘크리트 교각의 지진손상 평가 II : 수치해석 예

연계논문에서는 철근콘크리트 교각의 지진손상 평가를 위한 비선형 유한요소해석 기법을 제시하였다. 이 논문에서는 철근콘크리트 교각의 이력거동의 예측에 근거한 손상지수를 제시하였다. 손상지수는 지진하중하의 철근콘크리트 교각의 손상을 수치적으로 정량화하는 방법으로서 제안되었다. 제안한 해석기법을 실험된 철근콘크리트 교각에 적용하였고 다른 연구자의 손상지수와 비교.분석하였다. 제안된 해석기법은 조사된 실험체에 대하여 하중단계에 따라 손상을 정확하게 예측하였다. In the companion paper, nonlinear finite element analysis procedures are presented for the seismic damage evaluation of RC bridge piers. This paper defines a damage index based on the predicted hysteretic behavior of a RC bridge pier. Damage indices aim to provide a means of quantifying numerically the damage in RC bridge piers sustained under earthquake loading. The proposed numerical method is applied to RC bridge piers tested by other, and compared to existing damage indices. The proposed numerical method gives a realistic prediction of damage throughout the loading cycles for several test specimens investigated.

Effects of imperfections on the buckling response of compression-loaded composite shells

The results of an experimental and analytical study of the effects of initial imperfections on the buckling and postbuckling response of three unstiffened thin-walled compression-loaded graphite-epoxy cylindrical shells with different orthotropic and quasi-isotropic shell-wall laminates are presented. The results identify the effects of traditional and non-traditional initial imperfections on the non-linear response and buckling loads of the shells. The traditional imperfections include the geometric shell-wall mid-surface imperfections that are commonly discussed in the literature on thin shell buckling. The non-traditional imperfections include shell-wall thickness variations, local shell-wall ply-gaps associated with the fabrication process, shell-end geometric imperfections, non-uniform applied end loads, and variations in the boundary conditions including the effects of elastic boundary conditions. A high-fidelity non-linear shell analysis procedure that accurately accounts for the effects of these traditional and non-traditional imperfections on the non-linear responses and buckling loads of the shells is described. The analysis procedure includes a non-linear static analysis that predicts stable response characteristics of the shells and a non-linear transient analysis that predicts unstable response characteristics.

Discovery of superior enzymes by directed molecular evolution.

Natural selection has created optimal catalysts that exhibit their convincing performance even with a number of sometimes counteracting constraints. Optimal performance of enzyme catalysis does not refer necessarily to maximum reaction rate. Rather, it may involve a compromise between specificity, rate, stability, and other chemical constraints ; in some cases, it may involve aintelligento control of rate and specificity. Because enzymes are capable of catalyzing reactions under mild conditions and with high substrate specificity that often is accompanied by high regioand enantioselectivity, it is not surprising that a continually increasing number of industrial and academic reports concern the use of enzyme catalysts in chemical synthesis as well as in biochemical and biomedical applications. However, the demands of modern synthesis and their commercial application were obviously not targeted during the natural evolution of enzymes. Considering a specific, nonnatural application, any property (or combination of properties) of an enzyme may therefore need to be improved. Of course, scientists desired to mimick nature's powerful concepts for tailoring specific enzymatic properties: Following pioneering experiments for evolving molecules in the test tube, evolutionary engineering of biomolecules was successfully realized with first selections of functional nucleic acids (ribozymes) by using the SELEX (systematic evolution of ligands by exponential enrichment with integrated optimization by non-linear analysis) procedure, 8] and with the development of high-affinity ligands (aptamers) by using similar techniques. Meanwhile, evolutionary engineering, also termed adirected evolutiono, has emerged as a key technology for biomolecular engineering and generated impressive results in the functional adaptation of enzymes to artificial environments. Certainly, evolution in the laboratory does not come to a halt at the optimization of single genes and proteins. Recent results excitingly demonstrate the success of amolecular breedingo of metabolic pathways, and even of complete genomes, and the end is not in sight yet. Directed evolution in the laboratory is highly attractive because its principles are simple and do not require detailed knowledge of structure, function, or mechanism. Essentially like natural evolution, directed evolution comprises the iterative implementation of (1) the generation of a alibraryo of mutated genes, (2) its functional expression, and (3) a sensitive assay to identify individuals showing the desired properties, either by selection or by screening (Figure 1). After each round, the genes of improved variants are deciphered and subsequently serve as parents for another round of optimization. This review covers the most important aspects of directed evolution and summarizes key solutions to problems of optimizing and understanding enzyme function.

Second-order analysis of planar steel frames considering the effect of spread of plasticity

This paper presents a method of elastic-plastic analysis for planar steel frames that provides the accuracy of distributed plasticity methods with the computational efficiency that is greater than that of distributed plasticity methods but less than that of plastic-hinge based methods. This method accounts for the effect of spread of plasticity accurately without discretization through the cross-section of a beam-column element, which is achieved by the following procedures. First, nonlinear equations describing the relationships between generalized stresses and strains of the cross-section are derived analytically. Next, nonlinear force-deformation relationships for the beam-column element are obtained through lengthwise integration of the generalized strains. Elastic-plastic flexibility coefficients are then calculated by differentiating the above element force-deformation relationships. Finally, an elastic-plastic stiffness matrix is obtained by making use of the flexibility-stiffness transformation. Adding the conventional geometric stiffness matrix to the elastic-plastic stiffness matrix results in the tangent stiffness matrix, which can readily be used to evaluate the load carrying capacity of steel frames following standard nonlinear analysis procedures. The accuracy of the proposed method is verified by several examples that are sensitive to the effect of spread of plasticity.

Generalized Appended Product Indicator Procedure for Nonlinear Structural Equation Analysis

Interest in considering nonlinear structural equation models is well documented in the behavioral and social sciences as well as in the education and marketing literature. This article considers estimation of polynomial structural models. An existing method is shown to have a limitation that the produced estimator is inconsistent for most practical situations. A new procedure is introduced and defined for a general model using products of observed indicators. The resulting estimator is consistent without assuming any distributional form for the underlying factors or errors. Identification assessment and standard error estimation are discussed. A simulation study addresses statistical issues including comparisons of discrepancy functions and the choice of appended product indicators. Application of the new procedure in a substance abuse prevention study is also reported.

Development and Application of a Nonlinear Modal Analysis Technique for MDOF Systems

This work presents a frequency-domain technique that extends the concept of linear modal super position to nonlinear systems by using the normal nonlinear mode approach so that a generalized parameter identification method can be formulated for MDOF nonlinear systems. The methodology is compatible with existing established vibration analysis techniques such as finite element (FE) modeling and experimental modal analysis. Furthermore, once the nonlinear modal parameters are identified at some reference force level, the nonlinear response can be predicted at any arbitrary excitation level using standard modal sum mation techniques. The numerical study is focused on a 4-DOF system with friction damping nonlinearity, for which both the macro- and microslip representations are considered. Simulated nonlinear frequency re sponse functions, obtained for a given excitation level using a harmonic balance method, were subjected to a nonlinear modal analysis procedure, and the modal parameters were extracted as a function of the vibration amplitude. Micro- and macroslip representations yielded significantly different nonlinear modal parameters, though the findings were consistent with those of other researchers. The nonlinear modal analysis results and the response predictions at arbitrary forcing levels were compared against reference harmonic balance sim ulations, and very good agreement was observed for all cases investigated. It was verified that the friction damper produced highest damping for the vibration amplitude of maximum energy dissipation.

A Simplified Nonlinear Analysis Procedure for Single-Story Asymmetric Buildings Subjected to Strong Ground Motion

A Simplified Nonlinear Analysis Procedure for Single-Story Asymmetric Buildings Subjected to Strong Ground Motion

Shape Design Sensitivity Analysis and Optimization of Elasto-Plasticity with Frictional Contact

A shape design sensitivity analysis and optimization are proposed for the ine nitesimal elasto ‐plasticity with a frictional contact condition. Rate-independent plasticity is considered with a return mapping algorithm and a von Mises yield criterion. The contact condition is formulated using the penalty method and the modie ed coulomb friction law. A continuum-based shape design sensitivity formulation is developed for structural and frictional contact variational equations. The direct differentiation method is used to compute the displacement sensitivity, and the sensitivities of various performance measures are computed from the displacement sensitivity. Path dependency of the sensitivity equation due to the constitutive relation and friction is discussed. It is shown that no iteration is required to solve the sensitivity equation. Response analysis and the proposed sensitivity formulation are implemented using the mesh-free method where the mesh distortion problem can be resolved. Numerical examples show accurate results of the proposed method compared to the e nite difference method. Dife culties in the sensitivity formulation for the e nite deformation problem are discussed. I. Introduction B ECAUSEoftherecentdevelopmentofcomputationalmechanics, it is now possible to analyze practical examples of complicated structural problems. Many design engineers, who are not satise ed with response analysis alone, have keen interests in the methodology of the design. For more than two decades, signie cant research efforthasbeen focused on the rate of response with respect to the changes in structural shape under shape design sensitivity analysis (DSA). Analysis of the design sensitivity information is the most important and costly procedure in the automated optimum design process. It supplies useful quantitative information to the design engineer about the direction of the desired design change. In a classical linear problem, DSA research has proved the differentiability of the solution of the response analysis using the linear operator theory and has derived specie c sensitivity expressions for variousproblems. 1 Aresultworthy of attention in linear DSAis that theoriginalresponseandthesensitivityoftheresponsebelongtothe samekinematicallyadmissiblespaceandhavethesameregularities. Owing to the development of the response analysis capability, engineers have directed their interest to the nonlinear problems that are dealt with efe ciently. Because many design application problems are accompanied by plastic deformation, the design sensitivity of nonlinear problems has been actively developed, and many research results are reported. In the procedure of nonlinear response analysis, the projection, called a return mapping, of the elastic trial stress is carried out to satisfy the variational inequality (VI)through an iteration in the stress space. 2 The DSA, on the other hand, computes the rate of change of the projected response in the tangential direction of the constraint set without iteration. Note that the sensitivity analysis is linear and can be computed without iteration even thoughtheresponseanalysisisnonlinear. 3 Unlikethenonlinearelastic problem, the sensitivity equation of the plastic problem requires sensitivity of the stress and internal evolution variables at the previous time. The sensitivity equation is solved at each time without iteration, and the sensitivity of the stress and evolution variables are

A Nonlinear Analysis Method for Performance-Based Seismic Design

A relatively simple nonlinear method for the seismic analysis of structures (the N2 method) is presented. It combines the pushover analysis of a multi-degree-of-freedom (MDOF) model with the response spectrum analysis of an equivalent single-degree-of-freedom (SDOF) system. The method is formulated in the acceleration-displacement format, which enables the visual interpretation of the procedure and of the relations between the basic quantities controlling the seismic response. Inelastic spectra, rather than elastic spectra with equivalent damping and period, are applied. This feature represents the major difference with respect to the capacity spectrum method. Moreover, demand quantities can be obtained without iteration. Generally, the results of the N2 method are reasonably accurate, provided that the structure oscillates predominantly in the first mode. Some additional limitations apply. In the paper, the method is described and discussed, and it basic derivations are given. The similarities and differences between the proposed method and the FEMA 273 and ATC 40 nonlinear static analysis procedures are discussed. Application of the method is illustrated by means of an example.

Nonlinear deformation analysis of a U-shaped bellows with varying thickness

The nonlinear integral equations for a U-shaped bellows with compressed angle and varying wall-thickness are derived according to the simplified Reissner theory of large deflection for revolution shells and integral-equation method. The iteration procedure for nonlinear analysis is developed by means of the integral equation iteration in conjunction with the gradient method. Numerical solutions for a U-shaped bellows under the action of axial compression force and internal pressure are obtained, which are compared with previous theories and experiments. The present results are shown to have a good accuracy, and may be applied directly to the design of bellows.

Detecting nonlinearity in psychological data: techniques and applications.

Modern graphical and computational techniques for detecting nonlinearity in psychological data sets are presented. These procedures allow researchers to determine the information complexity of temporal data, using physiological and psychological measurements, and to provide evidence for chaos in time series contaminated by measurement noise. Problems with noise reduction and appropriate experimental control, using surrogate time series, are discussed, and applications of the technology are illustrated, using response time, handwriting, and typing data sets. In an experimental application of appropriate nonlinear analysis procedures, the results of a time series prediction experiment confirm that some subjects are sensitive to chaos. In contrast to previous attempts demonstrating sensitivity to chaos, the experiment reported here employs surrogate series to control for linear stochastic aspects of the stimulus sequences, such as autocorrelation. Recommendations for the selection of appropriate software for performing nonlinear analyses are presented, including a comprehensive list of World-Wide Web sites offering such software.

Evaluation of Earthquake-Damaged Concrete and Masonry Wall Buildings

Efforts at improving earthquake recovery policies have been hampered by a lack of criteria and standards for evaluating and repairing damaged buildings. The Applied Technology Council has developed a performance-based methodology for the evaluation of earthquake-damaged concrete wall buildings and masonry wall buildings, recently published as FEMA 306/307/308. The methodology provides a way to quantify damage in terms of loss of seismic performance capability. It also provides guidelines for remedial measures to restore or improve seismic performance capability. In this methodology, the expected future seismic performance of a building is evaluated in its pre-event, damaged, and repaired conditions. Following the nonlinear static analysis procedure, displacement demands and capacities of the structure are used as indices of seismic performance. Identifying the governing mechanism of nonlinear deformation and the behavior mode of a structure and its components is shown to be a necessary first step towards evaluating expected seismic performance, interpreting indications of damage, and assessing their significance. The methodology provides a technical resource for understanding how buildings respond seismically on both global and component levels, and gives a basis for formulating post-earthquake policies.

Nonlinear Dynamic Finite Element Analysis of Composite Cylindrical Shells Considering Large Rotations

A new nonlinear finite element formulation is developed for the nonlinear dynamics of shell structures. Using a vectorial approach, the kinematics that can be used to describe very large displacements and large rotations are derived. Green strain measures and second Piola Kirchhoff stress measures are used in the determination of the total potential. A displacement-based eight-noded cylindrical shell element with a total of 36 degrees of freedom is developed. Several numerical examples are dynamically analyzed to observe the characteristics of large displacements and large rotations. A convergence study was carried out to establish the numerical accuracy of the model. The most efficient and accurate model was used. HE nonlinear vibration analysis of shells has been the focus of research for the past few years. Thin shells subjected to dynamic loads could encounter deflections of the order of the thick- ness of the shell. Dynamic response of thin shells also could lead to the phenomena of dynamic snapping or dynamic buckling. Be- cause these kinds of responses cannot be determined accurately using small displacement and small rotation theories, large defor- mation and large rotation theories are required. The complex nature of these theories requires solving numerous simultaneous, nonlin- ear, differential equations. Even with simplifying assumptions, these equations remain complex and extensive. As background, a few relevant past efforts are reviewed. Earlier work regarding the nonlinear vibrations for isotropic shell structures can be attributed to Carr, 1 Yeh,2 Clough and Wilson,3 Belytschko and Marchertas,4 and Belytschko and Tsay.5 These researchers used flat plate elements. Saigal and Yang6 developed a curved shell element for isotropic shells. For composite shell structures, Simitses7 provided an elegant analytical solution of thin laminated shells subjected to sudden loads. He ignored through-the-thickness shear effects and used Donnell-type kinematic relations. Raouf and Palazotto8'9 developed a perturbation procedure to derive a set of asymptotically consistent nonlinear equations of motion for an arbi- trary laminated composite cylindrical shell in cylindrical bending. They also neglected transverse shear effects. Simo and Tarnow10 de- veloped an energy and momentum conservating algorithm for shell analysis to analyze shells undergoing large rigid-body motions. Palazotto and Dennis11 presented the simplified large rotation (SLR) theory to analyze shells experiencing moderately large ro- tations. The SLR theory determines the equilibrium path of or- thotropic shells using a total Lagrangian approach and includes a parabolic transverse shear stress distribution. This approach cap- tures the appropriate kinematics through displacement polynomi- als. Green strain displacement relations are used, and all of the final displacement functions are carried into the expression for the total potential without making any attempt at separating the rigid- body movement. Using this approach, the features classically pre- sented for, including through-the-thickness shear (for example), can be exploited.12 Smith and Palazotto13 discussed eight higher-order shear theories to the nonlinear finite element analysis of compos- ite shells. They also used the Green-Lagrange strains and second Piola Kirchhoff stresses. These theories were successful for large displacements and moderately large rotations. A reason for the fail- ure of these theories in the modeling of large rotation can be at- tributed to the approximations used in the kinematics. Gummadi and Palazotto14 modified the kinematics incorporated in the SLR theory and successfully carried out the solutions to problems ex- hibiting the characteristics of very large displacements and rota- tions. In their work, a vectorial approach was followed to derive the appropriate kinematics that can capture the characteristics of large displacements and large rotations. Using appropriate assumptions, the kinematics for the SLR theory can be obtained as a special case. The large rotation kinematics was introduced through the use of sine and cosine functions. A 36-degree-of-freedom composite shell element was developed based on this theory. Based on the SLR theory, Tsai and Palazotto15 formulated a nonlinear dynamic finite element analysis procedure for composite cylindrical shells. In their work, a linear mass matrix was incorpo- rated along with the nonlinear stiffness matrix that was originally developed in SLR theory. This theory again has the same drawbacks as the SLR theory in terms of realizing the large displacements and large rotations. In the present paper, a theory that can capture the large displacement and large rotations is discussed. The present work is an extension of the authors' earlier work on large rotation theory for static analysis. A new mass matrix is generated using Hamilton equations. The mass matrix thus generated is a nonlin- ear mass matrix. A fi-M method15 is used to solve the nonlinear algebraic equations resulting from the finite element technique. Se- lected numerical examples are solved to determine the validity of the developed theory.

Fundamental considerations for the design of non‐linear viscous dampers

An Erratum has been published for this article in Earthquake Engineering and Structural Dynamics 2000; 29(7):1076. Two interrelated issues related to the design of non-linear viscous dampers are considered in this paper: structural velocities and equivalent viscous damping. As the effectiveness of non-linear viscous dampers is highly dependent on operating velocities, it is important to have reliable estimates of the true velocity in the device. This should be based on the actual relative structural velocity and not the commonly misused spectral pseudo-velocity. This is because if spectral pseudo-velocities (PSV) are used, they are based on design displacements (Sv=ω0Sd) and are thus fundamentally different from the actual relative structural velocity. This paper examines the difference between these two velocities, and based on an extensive study of historical earthquake motions proposes empirical relations that permit the designer to transform the well-known spectral pseudo-velocity to an actual relative structural velocity for use in design. Non-linear static analysis procedures recommended in current guidelines for the design of structural systems with supplement damping devices are based on converting rate-dependent device properties into equivalent viscous damping properties based on an equivalent energy consumption approach. Owing to the non-linear velocity dependence of supplemental devices, an alternative approach for converting energy dissipation into equivalent viscous damping is advanced in this paper that is based upon power consumption considerations. The concept of a normalized damper capacity (ϵ) is then introduced and a simple design procedure which incorporates power equivalent linear damping based on actual structural velocities is presented. Copyright © 1999 John Wiley & Sons, Ltd.