Relationships between femoral strength evaluated by nonlinear finite element analysis and BMD,material distribution and geometric morphology

Precisely quantifying the strength of the proximal femur and accurately assessing hip fracture risk would enable those at high risk to be identified so that preventive interventions could be taken.Development of better measures of femoral strength using the clinically

Analytical study of performance evaluation for seismic retrofitting of reinforced concrete building using 3D dynamic nonlinear finite element analysis

This paper presents three-dimensional finite element （FE） analyses of an all-frame model of a three-story reinforced concrete （RC） building damaged in the 1999 Taiwan Chi-Chi Earthquake. Non-structural brick walls of the building acted as a seismic resistant element although their contributions were neglected in the design. Hence, the entire structure of a typical frame was modeled and static and dynamic nonlinear analyses were conducted to evaluate the contributions of the brick walls. However, the results of the analyses were considerably overestimated due to coarse mesh discretizations, which were unavoidable due to limited computer resources. This study corrects the overestimations by modifying （1） the tensile strengths and （2） shear stiffness reduction factors of concrete and brick. The results indicate that brick walls improve frame strength although shear failures are caused in columns shortened by spandrel walls. Then, the effectiveness of three types of seismic retrofits is evaluated. The maximum drift of the first floor is reduced by 89.3%, 94.8%, and 27.5% by Steel-confined, FuI1-RC, and Full-brick models, respectively. Finally, feasibility analyses of models with soils were conducted. The analyses indicated that the soils elongate the natural period of building models although no significant differences were observed.

Arc-length technique for nonlinear finite element analysis

Nonlinear solution of reinforced concrete structures, particularly complete load-deflection response, requires tracing of the equilibrium path and proper treatment of the limit and bifurcation points. In this regard, ordinary solution techniques lead to instability near the limit points and also have problems in case of snap-through and snap-back. Thus they fail to predict the complete load-displacement response. The arc-length method serves the purpose well in principle, received wide acceptance in finite element analysis, and has been used extensively. However modifications to the basic idea are vital to meet the particular needs of the analysis. This paper reviews some of the recent developments of the method in the last two decades, with particular emphasis on nonlinear finite element analysis of reinforced concrete structures.

INCREMENTAL ANALYSIS FOR NONLINEAR RUBBER-LIKE MATERIALS BY HYBRID STRESS FINITE ELEMENT

In this paper, on the basis of the incremental Reissner variational principle.a nonlinear finite element analysis has been accomplished and a formulation of hybrid stress element has been presented for incompressible Mooney rubber-like materials. The corrected terms of the non-equilibrium force and the incompressibility deviation are considered in the formulation. The computed values of numerical example agree very closely with the exact solution.

Nonlinear Finite Element Analysis of Paper Movement in Air

In order to improve the office paper feeder design, and eliminate paper jam fault in running office equipment, the static deformation and dynamic response of paper were analyzed by use of the Finite Element Method (FEM). In the analysis, the three nodes mangle plate and shell element were employed, and finite element incremental formulations were derived on the basis of Updated Lagrangian (U.L) description. The newmark method was used to analyze the transient response of paper. All the results calculated in this article coincide with those by experiments.

Nonlinear Finite Element Analysis of Ocean Cables

This study has focused on developing numerical procedures for the dynamic nonlinear analysis of cable structures subjected to wave forces and ground motions in the ocean. A geometrically nonlinear finite element procedure using the isoparametric curved cable element based on the Lagrangian formulation is briefly summarized. A simple and accurate method to determine the initial equilibrium state of cable systems associated with self-weights, buoyancy and the motion of end points is presented using the load incremental method combined with penalty method. Also the Newmark method is used for dynamic nonlinear analysis of ocean cables. Numerical examples are presented to validate the present numerical method.

Assessment of natural frequency of installed offshore wind turbines using nonlinear finite element model considering soil-monopile interaction

A nonlinear finite element model is developed to examine the lateral behaviors of monopiles, which support offshore wind turbines(OWTs) chosen from five different offshore wind farms in Europe. The simulation is using this model to accurately estimate the natural frequency of these slender structures, as a function of the interaction of the foundations with the subsoil. After a brief introduction to the wind power energy as a reliable alternative in comparison to fossil fuel, the paper focuses on concept of natural frequency as a primary indicator in designing the foundations of OWTs. Then the range of natural frequencies is provided for a safe design purpose. Next, an analytical expression of an OWT natural frequency is presented as a function of soil-monopile interaction through monopile head springs characterized by lateral stiffness KL, rotational stiffness KRand cross-coupling stiffness KLRof which the differences are discussed. The nonlinear pseudo three-dimensional finite element vertical slices model has been used to analyze the lateral behaviors of monopiles supporting the OWTs of different wind farm sites considered. Through the monopiles head movements(displacements and rotations), the values of KL, KRand KLRwere obtained and substituted in the analytical expression of natural frequency for comparison. The comparison results between computed and measured natural frequencies showed an excellent agreement for most cases. This confirms the convenience of the finite element model used for the accurate estimation of the monopile head stiffness.

Experimental and Finite Element Analysis for Multi-lead Rubber Bearings:A Comparative Study

The mechanical properties of multi-lead rubber bearings （MLRBs） were investigated by experiment and finite element analysis. First, the vertical stiffness, horizontal stiffness and yielded shear force were tested for four MLRB specimens and two specimens of the single-lead rubber bearings （ SLRBs）. Then, the MLRBs were modeled by the explicit finite element analysis software ANSYS/ LS-DYNA, in order to evaluate the horizontal force-displacement hysteretic curves under static vertical and dynamical horizontal loadings. The disagreement between the tested and theoretical values was less than 11.4%, and MLRBs and SLRBs were similar in vertical stiffness, pre-yield stiffness and yield stiffness.

Self-adaptive one-dimensional nonlinear finite element method based on element energy projection method

The element energy projection （EEP） method for computation of super- convergent resulting in a one-dimensional finite element method （FEM） is successfully used to self-adaptive FEM analysis of various linear problems, based on which this paper presents a substantial extension of the whole set of technology to nonlinear problems. The main idea behind the technology transfer from linear analysis to nonlinear analysis is to use Newton＇s method to linearize nonlinear problems into a series of linear problems so that the EEP formulation and the corresponding adaptive strategy can be directly used without the need for specific super-convergence formulation for nonlinear FEM. As a re- sult, a unified and general self-adaptive algorithm for nonlinear FEM analysis is formed. The proposed algorithm is found to be able to produce satisfactory finite element results with accuracy satisfying the user-preset error tolerances by maximum norm anywhere on the mesh. Taking the nonlinear ordinary differential equation （ODE） of second-order as the model problem, this paper describes the related fundamental idea, the imple- mentation strategy, and the computational algorithm. Representative numerical exam- ples are given to show the efficiency, stability, versatility, and reliability of the proposed approach.

THEORY OF PERTURBATION FINITE ELEMENT ANALYSIS FOR SOLUTION OF NONLINEAR BUCKLING CRITICAL LOADS OF STRUCTURES

The author presents a theory, including the complete analysis and incomplete analysis,of perturbational finite element analysis for the solution of nonlinear buckling critical loadsof structures.

Large-scale two-dimensional nonlinear FE analysis on PGA amplification effect with depth and focusing effect of Fuzhou Basin

Based on the explicit finite element(FE) method and platform of ABAQUS,considering both the inhomogeneity of soils and concave-convex fluctuation of topography,a large-scale refined two-dimensional(2D) FE nonlinear analytical model for Fuzhou Basin was established.The peak ground motion acceleration(PGA) and focusing effect with depth were analyzed.Meanwhile,the results by wave propagation of one-dimensional(1D) layered medium equivalent linearization method were added for contrast.The results show that:1) PGA at different depths are obviously amplified compared to the input ground motion,amplification effect of both funnel-shaped depression and upheaval areas(based on the shape of bedrock surface) present especially remarkable.The 2D results indicate that the PGA displays a non-monotonic decreasing with depth and a greater focusing effect of some particular layers,while the 1D results turn out that the PGA decreases with depth,except that PGA at few particular depth increases abruptly; 2) To the funnel-shaped depression areas,PGA amplification effect above 8 m depth shows relatively larger,to the upheaval areas,PGA amplification effect from 15 m to 25 m depth seems more significant.However,the regularities of the PGA amplification effect could hardly be found in the rest areas; 3) It appears a higher regression rate of PGA amplification coefficient with depth when under a smaller input motion; 4) The frequency spectral characteristic of input motion has noticeable effects on PGA amplification tendency.

Dynamic analysis and nonlinear identification of space deployable structure

The dynamic equivalent continuum modeling method of the mast which is based on energy equivalency principle was investigated. And three kinds of mast dynamic model were established, which were equivalent continuum model, finite element model and simulation model, respectively. The mast frequencies and mode shapes were calculated by these models and compared with each other. The error between the equivalent continuum model and the finite element model is less than 5% when the mast length is longer. Dynamic responses of the mast with different lengths are tested, the mode frequencies and mode shapes are compared with finite element model. The mode shapes match well with each other, while the frequencies tested by experiments are lower than the results of the finite element model, which reflects the joints lower the mast stiffness. The nonlinear dynamic characteristics are presented in the dynamic responses of the mast under different excitation force levels. The joint nonlinearities in the deployable mast are identified as nonlinear hysteresis contributed by the coulomb friction which soften the mast stiffness and lower the mast frequencies.

Analysis on nonlinear wind-induced dynamic response of membrane roofs with aerodynamic effects

Based on the characteristics of membrane structures and the air influence factors,this paper presented a method to simulate the air aerodynamic force effects including the added air mass,the acoustic radiation damping and the pneumatic stiffness.The infinite air was modeled using the acoustic fluid element of commercial FE software and the finite element membrane roof models were coupled with fluid models.A comparison between the results obtained by FE computation and those obtained by the vibration experiment for a cable-membrane verified the validity of the method.Furthermore,applying the method to a flat membrane roof structure and using its wind tunnel test results,the analysis of nonlinear wind-induced dynamic responses for such geometrically nonlinear roofs,including the roof-air coupled model was performed.The result shows that the air has large influence on vibrating membrane roofs according to results of comparing the nodal time-history displacements,accelerations and stress of the two different cases.Meantime,numerical studies show that the method developed can successfully solve the nonlinear wind-induced dynamic response of the membrane roof with aerodynamic effects.

Seismic Deformation and Seismic Resistance Analysis of Shapai Roller Compacted Concrete Arch Dam Based on Field Monitoring and Dynamic Finite Element Method

Shapai Roller Compacted Concrete(RCC) Arch Dam is the highest RCC arch dam of the 20th century in the world with a maximum height of 132m,and it is the only concrete arch dam near the epicentre of Wenchuan earthquake on May 12th,2008.The seismic damage to the dam and the resistance of the dam has drawn great attention.This paper analyzed the response and resistance of the dam to the seismic wave using numerical simulations with comparison to the monitored data.The field investigation after the earthquake and analysis of insitu data record showed that there was only little variation in the opening size at the dam and foundation interface,transverse joints and inducing joints before and after the earthquake.The overall stability of the dam abutment resistance body was quite good except a little relaxation was observed.The results of the dynamic finite element method(FEM) showed that the sizes of the openings obtained from the numerical modeling are comparable with the monitored values,and the change of the opening size is in millimeter range.This study revealed that Shapai arch dam exhibited high seismic resistance and overload capacity in the Wenchuan earthquake event.The comparison of the monitored and simulated results showed that the numerical method applied in this paper well simulated the seismic response of the dam.The method could be useful in the future application on the safety evaluation of RCC dams.

Nonlinear finite-element-based structural system failure probability analysis methodology for gravity dams considering correlated failure modes

The structural system failure probability(SFP) is a valuable tool for evaluating the global safety level of concrete gravity dams.Traditional methods for estimating the failure probabilities are based on defined mathematical descriptions,namely,limit state functions of failure modes.Several problems are to be solved in the use of traditional methods for gravity dams.One is how to define the limit state function really reflecting the mechanical mechanism of the failure mode;another is how to understand the relationship among failure modes and enable the probability of the whole structure to be determined.Performing SFP analysis for a gravity dam system is a challenging task.This work proposes a novel nonlinear finite-element-based SFP analysis method for gravity dams.Firstly,reasonable nonlinear constitutive modes for dam concrete,concrete/rock interface and rock foundation are respectively introduced according to corresponding mechanical mechanisms.Meanwhile the response surface(RS) method is used to model limit state functions of main failure modes through the Monte Carlo(MC) simulation results of the dam-interface-foundation interaction finite element(FE) analysis.Secondly,a numerical SFP method is studied to compute the probabilities of several failure modes efficiently by simple matrix integration operations.Then,the nonlinear FE-based SFP analysis methodology for gravity dams considering correlated failure modes with the additional sensitivity analysis is proposed.Finally,a comprehensive computational platform for interfacing the proposed method with the open source FE code Code Aster is developed via a freely available MATLAB software tool(FERUM).This methodology is demonstrated by a case study of an existing gravity dam analysis,in which the dominant failure modes are identified,and the corresponding performance functions are established.Then,the dam failure probability of the structural system is obtained by the proposed method considering the correlation relationship of main failure modes on the basis of the mechanical mechanism analysis with the MC-FE simulations.

Full－range nonlinear analysis of fatigue behaviors of reinforced concrete structures by finite element method

The offshore reinforced concrete structures are always subject to cyclic load, such as wave load.In this paper a new finite element analysis model is developed to analyze the stress and strain state of reinforced concrete structures including offshore concrete structures, subject to any number of the cyclic load. On the basis of the anal ysis of the experimental data,this model simplifies the number of cycles-total cyclic strain curve of concrete as three straight line segments,and it is assumed that the stress-strain curves of different cycles in each segment are the same, thus the elastoplastic analysis is only needed for the first cycle of each segment, and the stress or strain corresponding to any number of cycles can be obtained by superposition of stress or strain obtained by the above e lastoplastic analysis based on the cyclic numbers in each segment.This model spends less computer time,and can obtain the stress and strain states of the structures after any number of cycles.The endochronic-damage and ideal offshore concrete platform subject to cyclic loading are experimented and analyzed by the finite element method based on the model proposed in this paper. The results between the experiment and the finite element analysis are in good agreement,which demonstrates the validity and accuracy of the proposed model.

Finite element analysis on deformation of high embankment in heavy-haul railway subjected to freeze-thaw cycles

Finite element simulations are increasingly providing a versatile environment for this topic. In this study, a two-dimensional finite element analysis is conducted to predict the deformation of high embankment in Bazhun heavy-haul railway, China. A recently developed nonlinear softening-type constitutive model is utilized to model the be- havior of subgrade filling materials subjected to freeze-thaw cycles. For the convenience of practical application, the dynamic loading induced by a vehicle is treated as a quasi-static axle load. The deformation of this embankment with different moisture content under freeze-thaw cycles is compared. The results show that when subjected to the first freeze-thaw cycle, the embankment experienced significant deformation variations. Maximum deformation was usually achieved after the embankment with optimum moisture content experienced six freeze-thaw cycles, however, the em- bankment with moisre content of 8.0% and 9.5% deforms continuously even after experiencing almost ten freeze-thaw cycles. Overall, this study provides a simple nonlinear finite element approach for calculating the deformation of the embankment in changing climate conditions.

A Kind of Super-parametric Finite Element for Geometric Nonlinear Analysis of Plates and Shells

A new kind of super parametric finite elements for geometric nonlinear analysis of plates and shells is presented.Besides the nodes on the middle surface, additional virtual nodes are used to determine the normal to the middle surface.There are three displacement d.o.f.for each node of the element, and two transverse shear strains are taken as additional independent d.o.f.for each node on the middle surface.Therefore, the element is suitable for large rotation analysis of plates and shells. It can also be easily applied to the analysis of laminated and sandwich shells and plates.Numerical examples are given to show the accuracy and efficiency of the element.

Bubble-enhanced quadrilateral finite element formulation for nonlinear analysis of geotechnical problems

We investigate a new numerical procedure based on a bubble-enriched finite element formulation in combination with the implicit backward Euler scheme for nonlinear analysis of strip footings and stability of slopes.The soil body is modeled as a perfect plastic Mohr-Coulomb material.The displacement field is approximated by a 4-node quadrilateral element discretization enhanced with bubble modes.Collapse loads and failure mechanisms in cohesive frictional soil are determined by solving a few Newton-Raphson iterations.Numerical results of the present approach are verified by both analytical solutions and other numerical solutions available in the literature.

Nonlinear Bend Stiffener Analysis Using A Simple Formulation and Finite Element Method

Flexible marine risers are commonly used in deepwater floating systems. Bend stiffeners are designed to protect flexible risel against excessive bending at the connection with the hull. The structure is usually analyzed as a cantilever beam subjected to an inclined point load. As deflections are large and the bend stiffener material exhibits nonlinear stress-strain characteristics, geometric and material nonlinearities are important considerations. A new approach has been developed to solve this nonlinear problem. Its main advantage is its simplicity; in fact the present method can be easily implemented on a spreadsheet. Finite element analysis using ABAQUS is performed to validate the method. Solid elements are used for the bend stiffener and flexible pipe. To simulate the near inextensibility of flexible risers, a simple and original idea of using truss elements is proposed. Through a set of validation studies the present method is found to be in a good agreement with the finite element analysis. Further, parametric studies are performed by using both methods to identify the key parameters and phenomena that are most critical in design. The most important finding is that the common practice of neglecting the internal steel sleeve in the bend stiffener analysis is non-conservative and therefore needs to be reassessed.