Analytical Model for Geometric and Material Nonlinear Analysis of Externally Prestressed Beams

The analysis of beams prestressed by external slipping tendons involves various difficulties related to the coupling between the local strain of the tendons and the global deformation of the beam. The structural behavior of the beam–tendon system at collapse is ruled both by the nonlinearity of materials and by geometric nonlinear effects. Recent scientific papers have shown the relevance of the geometric effects in evaluating the failure load of externally prestressed beams by considering the tendon eccentricity variation. The change of eccentricity is however only one of the geometric nonlinear effects. In this work the writers present a complete geometric and mechanical nonlinear analytical model based on the theory of small strains and moderate rotations deduced from the finite deformation theory.     

Postbuckling of Shear Deformable Laminated Cylindrical Shells

A postbuckling analysis is presented for a shear deformable laminated cylindrical shell of finite length subjected to compressive axial loads. The governing equations are based on Reddy’s higher-order shear deformation shell theory with a von Kármán–Donnell type of kinematic nonlinearity. The nonlinear prebuckling deformations and initial geometric imperfections of the shell are both taken into account. A boundary layer theory of shell buckling, which includes the effects of nonlinear prebuckling deformations, large deflections in the postbuckling range, and initial geometric imperfections of the shell, is extended to the case of shear deformable laminated cylindrical shells under axial compression. A singular perturbation technique is employed to determine the buckling loads and postbuckling equilibrium paths. The numerical illustrations concern the postbuckling response of perfect and imperfect, unstiffened or stiffened, moderately thick, cross-ply laminated cylindrical shells. The effects of transverse shear deformation, shell geometric parameters, total number of plies, fiber orientation, and initial geometric imperfections are studied.     

Three-Dimensional Elastic Catenary Cable Element Considering Sliding Effect

The nonlinear behavior of cable-supported bridges is governed by the geometric nonlinearity of cables, which is attributable to sag and sliding effects at the saddle. In a cable-stayed bridge with a midspan saddle, and in all suspension bridges, cable sliding can occur at the saddle under extreme forces, such as those caused by an earthquake or typhoon. However, the conventional method of analysis of cable-supported bridges does not consider the effect of cable sliding at the saddle; instead it regards those cables as fixed. This assumption might lead to a misunderstanding of the global structure system. The goal of this study is to develop a three-dimensional (3D) elastic cable finite element that considers the sliding effect and uses a geometric nonlinear cable finite element based on elastic catenary theory. In this study, two types of sliding were considered: the roller sliding condition without friction and the frictional sliding condition. These were formulated to derive the nodal force vectors and tangential stiffness matrices. To validate the proposed 3D cable sliding element, experiments were conducted for both sliding conditions, and results were compared with calculations of the amount of sliding and displacement at the loading point. In addition, a cable-supported structural system was analyzed to investigate the characteristics of a realistic structure with cable sliding. Overall calculations using the 3D cable sliding model were in very good agreement with the measured values.     

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.     

Uncoupling of Potential Energy in Nonlinear Seismic Analysis of Framed Structures

A computational analysis method is presented to investigate the potential energy of fully nonlinear framed structures and other energy characteristics due to earthquake ground motions. The overall potential energy is directly related to the stiffness of the structure, and it consists of three components in a fully nonlinear system: (1) strain energy representing the storing energy that is associated with the linear elastic portion of the structural response; (2) higher-order energy representing the energy associated with the geometric nonlinear effect of the overall structural response, which is derived from finite element method; and (3) plastic energy representing the energy dissipated by material inelasticity of the structure, and it is being derived analytically. The merit of proposed analysis method lies in the uncoupling of geometric nonlinearity and material inelasticity effects before solving for the equation of motion, and this leads directly to the analytical representations of each energy form. Both plastic energy and higher-order energy based on single-degree-of-freedom system are studied in detail to demonstrate the beauty of the proposed analysis method. In addition, a method of generating energy density spectra is also proposed, which is useful to enhance the understanding energy characteristics in seismic analysis. Finally, a five-story frame is used as a numerical example to illustrate the effectiveness and robustness of the proposed method.     

Nonlinear Response of Laminated Cylindrical Shell Panels Subjected to Thermomechanical Loads

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

Effect of Stress‐Dependent Base Layer on the Superposition of Flexible Pavement Solutions

Flexible pavement structural analysis for design usage must consider (as a minimum) multiple wheel/axle loading configurations, seasonal variations of material layer properties, and the nonlinear behavior of unbound materials. Although these requirements are all easily within the capabilities of three‐dimensional finite element analysis, the required computation times may be impracticably long for routine design. Compromises between analytical rigor (e.g., three‐dimensionality) and analysis features (e.g., multiple wheels, seasonal property variations, material nonlinearity) must be made. One compromise is to retain seasonal property variations and material nonlinearity within an axisymmetric single wheel finite element model and to approximate multiple wheel effects via superposition. Although this superposition of nonlinear solutions is undeniably invalid from a rigorous theoretical viewpoint, the errors may be well within acceptable magnitudes for practical design. The paper investigates this issue by comparing superimposed nonlinear solutions against computationally rigorous three‐dimensional nonlinear solutions and evaluating the discrepancies in key pavement response quantities. The results suggest that the errors from superimposing nonlinear solutions are acceptably small for key pavement response quantities. Moreover, these errors are substantially smaller than those resulting from neglect of nonlinear unbound material behavior, a modeling compromise that is common in pavement structural analysis today.     

Earthquake Response of Elastic Single-Degree-of-Freedom Systems with Nonlinear Viscoelastic Dampers

Investigated are the steady-forced and earthquake responses of single-degree-of-freedom (SDF) systems with a nonlinear viscoelastic damper (VED), which consists of a nonlinear fluid viscous damper (FVD) connected in series to a linear elastic bracing element (chevron or inverted V-shaped braces). For a wide range of bracing stiffness, nonlinear dampers are advantageous because they achieve essentially the same reduction in system responses but with a significantly reduced force. Damper nonlinearity has little influence on the structural response in the velocity-sensitive region of the spectrum even if the bracing is fairly flexible, but differences up to 16% were observed in other spectral regions. As expected, supplemental damping reduces structural response and the response reduction depends on the bracing stiffness, with this dependence varying with the spectral regions. For practical applications, a procedure is presented to estimate the design values of structural deformation, structural force, foundation shear, and damper force directly from the earthquake design (or response) spectrum. Finally, a procedure is presented to determine the damper and bracing properties necessary to limit the structural deformation to some design value or to the structural capacity.     

Investigation of Geometric Imperfection in Inflatable Aerospace Structures

Communication and solar array inflated structures must be deployed to a very precise geometric configuration in order to meet quality requirements of their application. The focus of this paper is on geometric imperfections associated with inflated structures. To further understand some of the elements, that derive imperfection in a parabolic inflated communication and solar array structures, a computational model is proposed. This computational approach is dictated by the geometric complexity, deformation sensitivity as function of load and boundary conditions, and nonlinear characteristics of inflated structure assemblies. The deformation of a single component depends on the flexibility/stiffness of other components due to their interaction. In order to simulate such deformations of the multicomponent inflated structure, in the present study, the computational model consists of main parabolic shape envelope (reflector and canopy), torus, and catenary’s support and uses geometric nonlinear finite element. Further, tuning of communications and solar arrays is a primary concern in the operation of these systems. To investigate the effects of pressure tuning on geometric imperfection of a parabolic inflated antenna, in this investigation, analyses using uniformly axisymmetric and asymmetric applied load are performed. The analyses assume an initial parabolic shape envelope with a perfect circular edge for the reflector and canopy. Error estimates, which quantify geometric imperfections, are computed. The results show that as the axisymmetric load increases, the surface deviation from the parabolic shape of the envelope also increases. An asymmetric load on the surface of the torus leads to variable tensile forces in the catenary along the circular edge of the envelope, which in turn cause a visible local asymmetrical deformation in the vicinity of the circular edge of the envelope. In general, an asymmetric load causes greater geometric imperfections and should be avoided     

Postbuckling of Pressure-Loaded Functionally Graded Cylindrical Panels in Thermal Environments

A postbuckling analysis is presented for a functionally graded cylindrical panel of finite length subjected to lateral pressure in thermal environments. Material properties are assumed to be temperature dependent, and graded in the thickness direction according to a simple power-law distribution in terms of the volume fractions of the constituents. The governing equations of a functionally graded cylindrical panel are based on Reddy’s higher-order shear deformation shell theory with von Kármán–Donnell-type of kinematic nonlinearity and include thermal effects. The two straight edges of the panel are assumed to be simply supported and two curved edges are either simply supported or clamped. The nonlinear prebuckling deformations and initial geometric imperfections of the panel are both taken into account. A boundary layer theory of shell buckling, which includes the effects of nonlinear prebuckling deformations, large deflection in the postbuckling range, and initial geometric imperfections of the shell, is extended to the case of functionally graded cylindrical panels. A singular perturbation technique is employed to determine the buckling loads and postbuckling equilibrium paths. The numerical illustrations concern the postbuckling behavior of simply supported, pressure-loaded, perfect and imperfect, functionally graded cylindrical panels with two constituent materials under different sets of thermal environments. The influences played by temperature rise, volume fraction distributions, transverse shear deformation, panel geometric parameters, as well as initial geometric imperfections, are studied.     

钢包回转台连杆水平偏移机理的研究

采用三维非线性接触有限元技术,对钢包回转台连杆出现的明显水平偏移现象进行了研究,发现附加水平推力是产生水平偏移的主要原因,而不是倾翻力矩。通过分析得到的水平偏移的力学机理为:①填丝油封沿关节轴的轴向表现出弱接触刚度,在较小的附加水平推力作用下,可产生明显的接触变形;②连杆与关节轴结构装配方式导致形成了一个填丝油封接触变形的放大机构,从而引起连杆端部出现可观的水平偏移。根据研究结果,在生产现场采用隔垫调整连杆位置的技术措施,消除了油缸顶升产生的附加水平推力,从而纠正了连杆的明显水平偏移,有效地保证了钢包回转台的生产安全。     

Nonlinear Identification of Lumped-Mass Buildings Using Empirical Mode Decomposition and Incomplete Measurement

Most structures exhibit some degrees of nonlinearity such as hysteretic behavior especially under damage. It is necessary to develop applicable methods that can be used to characterize these nonlinear behaviors in structures. In this paper, one such method based on the empirical mode decomposition (EMD) technique is proposed for identifying and quantifying nonlinearity in damaged structures using incomplete measurement. The method expresses nonlinear restoring forces in semireduced-order models in which a modal coordinate approach is used for the linear part while a physical coordinate representation is retained for the nonlinear part. The method allows the identification of parameters from nonlinear models through linear least-squares. It has been shown that the intrinsic mode functions (IMFs) obtained from the EMD of a response measured from a nonlinear structure are numerically close to its nonlinear modal responses. Hence, these IMFs can be used as modal coordinates as well as provide estimates for responses at unmeasured locations if the mode shapes of the structure are known. Two procedures are developed for identifying nonlinear damage in the form of nonhysteresis and hysteresis in a structure. A numerical study on a seven-story shear-beam building model with cubic stiffness and hysteretic nonlinearity and an experimental study on a three-story building model with frictional magnetoreological dampers are performed to illustrate the proposed method. Results show that the method can quite accurately identify the presence as well as the severity of different types of nonlinearity in the structure.     

Model for the Force–Displacement Relationship of Wire Rope Springs

A mathematical model for the restoring force of the wire rope spring is presented. The model is semianalytical in nature and is fully defined by the dimensions and properties of the spring. Emphasis is placed on the tension-compression mode of deformation. An experimental investigation is described in which the force–displacement relationships, for a number of springs, were obtained. For modeling purposes, the restoring force is decomposed into an elastic force and a damping force. The elastic force is modeled by a geometric nonlinear finite beam element. The equivalent cross section is calculated assuming full slip among the individual wires and strands. The damping force is modeled by a constant and a displacement-dependent forces. Based on energy dissipation equivalence, an empirical expression for the damping force is developed.     

Composite Bars of Arbitrary Cross Section in Nonlinear Elastic Nonuniform Torsion by BEM

In this paper the elastic nonuniform torsion analysis of composite cylindrical bars of arbitrary cross section consisting of materials in contact, each of which can surround a finite number of inclusions, taking into account the effect of geometric nonlinearity is presented employing the boundary element method (BEM). All of the cross section’s materials are perfectly bonded together, that is separation is not allowed. The torque-rotation relationship is computed based on the finite displacement (finite rotation) theory, that is the transverse displacement components are expressed so as to be valid for large rotations and the longitudinal normal strain includes the second-order geometric nonlinear term often described as the “Wagner strain.” The proposed formulation does not stand on the assumption of a thin-walled structure and therefore the cross section’s torsional rigidity is evaluated exactly without using the so-called Saint-Venant’s torsional constant. The torsional rigidity of the cross section is evaluated directly employing the primary warping function of the cross section depending on its shape. Three boundary value problems with respect to the variable along the beam axis angle of twist, to the primary and to the secondary warping functions are formulated. The first one, employing the Analog Equation Method (a BEM based method), yields a system of nonlinear equations from which the angle of twist is computed by an iterative process. The rest two problems are solved employing a pure BE method. Numerical results are presented to illustrate the method and demonstrate its efficiency and accuracy. The developed procedure retains most of the advantages of a BEM solution over a pure domain discretization method, although it requires domain discretization.     

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

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

A model for the responses of low-frequency auditory-nerve fibers in cat

A computational model was developed for the responses of low-frequency auditory-nerve (AN) fibers in cat. The goal was to produce realistic temporal response properties and average discharge rates in response to simple and complex stimuli. Temporal and average-rate properties of AN responses change as a function of sound-pressure level due to nonlinearities in the auditory periphery. The input stage of the AN model is a narrow-band filter that simulates the mechanical tuning of the basilar membrane. The parameters of this filter vary continuously as a function of stimulus level via a feedback mechanism, simulating the compressive nonlinearity associated with the mechanics of the basilar membrane. A memoryless, saturating nonlinearity and two low-pass filters simulate transduction and membrane properties of the inner hair cell (IHC). A diffusion model for the IHC-AN synapse introduces adaptation. Finally, a nonhomogeneous Poisson process, modified by absolute and relative refractoriness, provides the output discharge times. Responses to several different stimuli are presented. These responses illustrate nonlinear temporal response properties that cannot be achieved with linear models for AN fibers.     

Immediate Settlement of Shallow Foundations Bearing on Clay

Immediate and long-term settlement checks are an integral part of foundation design. Therefore, reasonably accurate estimates of the immediate settlement of shallow foundations bearing on clay are necessary, particularly for highly plastic clays or organic soils, for which the immediate settlement may be significant. This immediate settlement is due entirely to the distortion of the clay underneath the shallow foundations because, in the short term, there is no opportunity for change in the clay volume. Since soil stress-strain response is nonlinear even at small strains, design procedures based on linear elasticity cannot accurately predict soil deformations. Hence, an immediate settlement analysis that takes soil nonlinearity into account is needed. In this paper, finite-element analysis is used to develop design charts that can be used to estimate the immediate settlement of axially loaded square, rectangular, and strip footings bearing on clay. The clay is modeled with a simple nonlinear constitutive relationship. A design example is included to illustrate how the proposed procedure can be readily applied in practice with the knowledge of the undrained shear strength and the initial shear modulus of the clay.     

Postbuckling Analysis of Plates Resting on a Tensionless Elastic Foundation

The buckling and large deflection postbuckling behavior of plates laterally constrained by a tensionless foundation and subjected to in-plane compressive forces are investigated. A nonlinear finite-element formulation based on Marguerre’s nonlinear shallow shell theory, modified by Mindlin’s hypothesis, is employed to model the plate response. To overcome difficulties in solving the plate–foundation equilibrium equations together with the inequality constraints due to the unilateral contact condition, two different approaches are used: (1) the unilateral constraint is accounted for indirectly by a bilinear constitutive law and (2) the problem is formulated as a mathematical programming problem with inequality constraints from which a linear complementarity problem is derived and solved by the Lemke algorithm. To obtain the nonlinear equilibrium paths, the Newton–Raphson algorithm is used together with path-following strategies. Plate–foundation interaction leads to interesting deformation sequences, characterized by the variation of the contact and noncontact zones along the postbuckling path, leading sometimes to sudden changes in the deformation pattern. The results have a remarkable dependence on the plate aspect ratio, foundation stiffness, and buckling shape. The effects of geometric imperfections on the nonlinear response of the plate are also investigated. From these results, a number of insightful conclusions regarding the behavior of such plate–foundation systems are drawn.     

钢轨万能精轧过程的三维弹塑性有限元模拟

借助有限元分析软件MSC.Marc,采用三维热-机耦合弹塑性有限元模型,对钢轨万能精轧过程进行模拟分析。以UR-EF-UF三机架连轧过程为研究对象,建立变形过程优化模型。将轧件尺寸模拟结果与实验结果进行比较,两者吻合较好,验证了模型的准确性。对轧件变形过程、轧制接触状态、应力应变分布以及速度变化等模拟结果进行了讨论分析,揭示了万能轧机各道次的加工特点和轧件在连轧变形过程的变形规律。     

Stochastic Analysis of a Single-Degree-of-Freedom Nonlinear Experimental Moored System Using an Independent-Flow-Field Model

Stochastic characteristics of the surge response of a nonlinear single-degree-of-freedom moored structure subjected to random wave excitations are examined in this paper. Sources of nonlinearity of the system include a complex geometric configuration and wave-induced quadratic drag. A Morison-type model with an independent-flow-field formulation and a three-term-polynomial approximation of the nonlinear restoring force is employed for its proven excellent prediction capability for the experimental results investigated. Wave excitations considered in this study include nearly periodic waves, which take into account the presence of tank noise, noisy periodic waves that have predominant periodic components with designed additive random perturbations, and narrow-band random waves. A unified wave excitation model is used to describe all the wave conditions. A modulating factor governing the degree of randomness in the wave excitations is introduced. The corresponding Fokker–Planck formulation is applied and numerically solved for the response probability density functions (PDFs). Experimental results and simulations are compared in detail via the PDFs in phase space. The PDFs portray coexisting multiple response attractors and indicate their relative strengths, and experimental response behaviors, including transitions and interactions, are accordingly interpreted from the ensemble perspective. Using time-averaged probability density functions as an invariant measure, probability distributions of large excursions in experimental and simulated responses to various random wave excitations are demonstrated and compared. Asymptotic long-term behaviors of the experimental responses are then inferred.