Computational stochastic structural analysis — a contribution to the software development for the reliability assessment of structures under dynamic loading

Mainly due to the lack of respective available procedures generally, traditional methods of analysis and design of engineering structures neglect the statistical, i.e. intrinsic, uncertainties of the parameters involved. As shown in the present paper, however, the treatment of complex systems becomes feasible by interrelating mechanical modeling procedures, e.g. by finite elements, with efficient and accurate stochastic analysis, e.g. Monte Carlo type simulation. Hence the suggested method, which is in fact based on the response surface procedures, allows the utilization of the respective most modern structural as well as stochastic analysis procedures. This, of course implies the total collapse failure criterion of structures under dynamic loading.     

Crashworthiness design of horsetail-bionic thin-walled structures under axial dynamic loading

Bio-inspired engineering design has drawn increased attention in recent years for the excellent structural and mechanical properties of the biological systems. In this study, the horsetail-bionic thin-walled structures (HBTSs) were investigated for their crashworthiness under axial dynamic loading. Six HBTSs with different cross section configurations (i.e., number of cells) were evaluated using nonlinear finite element (FE) simulations. To obtain the optimal design of the HBTSs, an ensemble metamodel-based multi-objective optimization method was employed to maximize the specific energy absorption while minimizing maximum impact force of the HBTSs. Using the ensemble metamodeling, FE simulations and the NSGA-II algorithm, the Pareto optimum designs of all six HBTSs were obtained and the HBTS with 16 cells were found to have the best crashworthiness. An optimum design of the HBTS with 16 cells was verified using FE simulation and found to have good agreement with simulation results.     

Reliability assessment of polysilicon MEMS structures under mechanical fatigue loading

This paper examines the current status and methodologies of study of material and system reliability in Microelectromechanical Systems (MEMS). This includes: a review of the current literature in the area of MEMS regarding failure analysis experimental investigations; testing methods and philosophies for material characterization and possible mechanistic analytical solutions for estimating material properties. The paper proposes a reliability framework that encompasses all the available information. This statistical platform will enable the MEMS design engineer to distill all the available information in the literature into a stand-alone semi-empirical material reliability model, and a holistic system-level model for a complete system.     

Time-domain seismic reliability of nonlinear structures

A novel reliability analysis technique is presented to estimate the reliability of real structural systems. Its unique feature is that the dynamic loadings can be applied in time domain. It is a nonlinear stochastic finite element logarithm combined with the response surface method (RSM). It generates the response surface around the most probable failure point and incorporates information of the distribution of the random variables in the RSM formulation. It is verified using the Monte Carlo simulation technique, and is found to be very efficient and accurate. Most sources of nonlinearlity and uncertainty can be explicitly incorporated in the formulation. The flexibility of connections, represented by moment-relative rotation(M-θ) curves, is addressed. After the Northridge earthquake of 1994, several improved steel connections were proposed. Structural Sesimic Design Associates (SSDA) tested several full-scale proprietory slotted web beam-column connections. The authors suggested(M-θ) curves for this connection using actual test data. Behaviours of steel frames, assuming the connections are fully restrained, partially restrained, consisting of pre and post-Northridge connections are evaluated and compared. Desirable features of the post-Northridge connections observed during testing are analytically confirmed. Laterally weak steel frame is then strengthened with concrete shear walls. Capabilities and the advanced nature of the method are demonstrated with the help of realistic examples. This paper is dedicated to Prof R N Iyengar of the Indian Institute of Science on the occasion of his formal retirement.     

Bidirectional evolutionary structural optimization for nonlinear structures under dynamic loads

This study aims to develop efficient numerical optimization methods for finding the optimal topology of nonlinear structures under dynamic loads. The numerical models are developed using the bidirectional evolutionary structural optimization method for stiffness maximization problems with mass constraints. The mathematical formulation of topology optimization approach is developed based on the element virtual strain energy as the design variable and minimization of compliance as the objective function. The suitability of the proposed method for topology optimization of nonlinear structures is demonstrated through a series of two- and three-dimensional benchmark designs. Several issues relating to the nonlinear structures subjected to dynamic loads such as material, geometric, and contact nonlinearities are addressed in the examples. It is shown that the proposed approach generates more reliable designs for nonlinear structures.     

Some theoretical considerations on the dynamic response of sandwich structures under impulsive loading

A theoretical solution is obtained to predict the dynamic response of peripherally clamped square metallic sandwich panels with either honeycomb core or aluminium foam core under blast loading. In the theoretical analysis, the deformation of sandwich structures is separated into three phases, corresponding to the transfer of impulse to the front face velocity, core crushing and overall structural bending/stretching, respectively. The cellular core is assumed to have a progressive crushing deformation mode in the out-of-plane direction, with a dynamically enhanced plateau stress (for honeycombs). The in-plane strength of the cellular core is assumed unaffected by the out-of-plane compression. By adopting an energy dissipation rate balance approach developed by earlier researchers for monolithic square plates, but incorporating a newly developed yield condition for the sandwich panels in terms of bending moment and membrane force, “upper” and “lower” bounds are obtained for the maximum permanent deflections and response time. Finally, comparative studies are carried out to investigate: (1) influence of the change in the in-plane strength of the core after the out-of-plane compression; (2) performances of a square monolith panel and a square sandwich panel with the same mass per unit area; and (3) analytical models of sandwich beams and circular and square sandwich plates.     

Initial and progressive failure analysis of laminated composite structures under dynamic loading

The problem of theoretical prediction of the initial failure and ply-by-ply failure processes in laminated composite structures under dynamic loading is under consideration. A history of deformation can be predicted at any point of a structure using the proposed analytical techniques. The phenometological. second-order tensor-polynomial and maximum stress failure criteria are used to calculate the lower bound of an applied dynamic load. This lower bound corresponds to a start of failure in a structural part. A ply-by-ply failure model is then developed. Using the model, some higher bound for a critical dynamic load impulse value, corresponding to the total exhaustion of a load-bearing capacity by all of the layers in a laminated structure can be predicted. The analysis is applied to thin-walled imperfect laminated graphite/epoxy cylindrical shells, loaded with a short-time impulse of axial compression or external pressure. A general approach to the 3D dynamic deformation analysis of a brick-type mosaic plate and its interaction with a rigid impactor is proposed The approach allows one to model both the initial and damage induced inhomogeneities in a composite structure under dynamic impulsive or impact loading cases.     

Fatigue reliability assessment of offshore structures

Substantial laboratory and field experience has indicated that, owing to the large number of wave stress cyles experienced by offshore steel structures, fatigue cracking should be the main consideration of structural reliability assessment. This paper presents the latest implementation of probabilistic fracture mechanics modelling for fatigue reliability analysis of the most common offshore structural component, the welded tubular joints. Coupled with the recent findings in inspection reliability, effective maintenance and integrity monitoring policies can be formulated. Examples of many practical situations have been analysed to illustrate the applications of the methodology.     

Fatigue reliability analysis under two-stage loading

On the basis of the two-dimensional probabilistic Miner's rule, a new method of fatigue reliability analysis under two-stage loading is established. Eight large samples of testing data under low–high and high–low two-stage cyclic loading are used in the experimental verification. It is showed that the reliability-based predictions of the residual fatigue life as well as of the total fatigue life agree very well with the experimental results.     

Aggregate breakage under dynamic loading

Numerical simulations with the Discrete Element Method are used to study agglomerate breakage under two different kinds of dynamic loading: normal impact and shear loading. Simple mechanical models based on energy balance are developed herein for each one and show good agreement with the results of the simulations. For impact, damage is found to depend on a dimensionless number N _i , which describes the ratio of the incoming kinetic energy to the internal bonding energy. For shear loading, damage is shown to depend on another dimensionless number N _f which describes the ratio of the frictional work to the internal bonding energy. The friction force is first modelled as a solid-like friction force, then the model is improved by using a granular frictional force. The two types of loading as damaging processes are then compared. These results appear to be consistent with the available experimental data on impact and abrasion wear tests.     

动载测试与小波分析在桥梁结构损伤诊断中的联合应用

将结构动载测试与小波分析相结合提出了适用于大跨桥梁结构的两阶段损伤诊断方法。采集桥梁结构在损伤前后各测点的动载测试数据并进行小波包分解得到小波包能量谱，在此基础上计算结构损伤预警指标和损伤定位指标，用以确定损伤的发生及其所在的区域。某三跨连续梁桥的数值模拟研究结果表明了本文所采用的损伤诊断方法的可行性与有效性。     

Fatigue reliability assessment for orthotropic steel deck details under traffic flow and temperature loading

A new fatigue reliability assessment function which takes into account the vehicle and temperature loadings has been developed in this study. The vehicle and temperature loadings are important parameters as they can cause fatigue failure of the welds in a steel box girder. The temperature affects the traffic loading effect by changing the elastic modulus of asphalt pavement. The effect of the temperature difference has been considered based on the measured data and the finite element analysis. Linear regression equations between the equivalent stress and the temperature for different vehicle types have been developed. Using the thermal stress analysis and the rain-flow counting method, the temperature difference fatigue stress spectrum has been determined. Further, a limit equation for the fatigue reliability assessment, which takes into account both the vehicle and temperature loadings, has been developed. Finally, the effects of the temperature and the traffic growth rate on the fatigue reliability of two welding types of Nan-xi Yangtze River Suspension Bridge have been assessed.     

Importance sampling for reliability assessment of dynamic systems under general random process excitation

This paper develops a reliability assessment method for dynamic systems subjected to a general random process excitation. Safety assessment using direct Monte Carlo simulation is computationally expensive, particularly when estimating low probabilities of failure. The Girsanov transformation-based reliability assessment method is a computationally efficient approach intended for dynamic systems driven by Gaussian white noise, and this approach can be extended to random process inputs that can be represented as transformations of Gaussian white noise. In practice, dynamic systems may be subjected to inputs that may be better modeled as non-Gaussian and/or non-stationary random processes, which are not easily transformable to Gaussian white noise. We propose a computationally efficient scheme, based on importance sampling, which can be implemented directly on a general class of random processes — both Gaussian and non-Gaussian, and stationary and non-stationary. We demonstrate that this approach is in fact equivalent to Girsanov transformation when the uncertain inputs are Gaussian white noise processes. The proposed approach is demonstrated on a linear dynamic system driven by Gaussian white noise and Brownian bridge processes, a multi-physics aero-thermo-elastic model of a flexible panel subjected to hypersonic flow, and a nonlinear building frame subjected to non-stationary non-Gaussian random process excitation.     

Long term random dynamic loading of concrete structures

Conclusion The results from numerous experiments indicate that the fatigue phenomenon cannot be connected to static strength. A specimen or a construction has a fatigue life limit. If the construction has endured some fatigue loading. The ability to take repeated loads is reduced regardless whether the static strength is increased or decreased. Our ability to predict the fatigue life of a structure is better than previously. Further improvement will probably be achieved by a more profound study of the progress of the changes during the fatigue loading so that the effect of variable repeated loads can be put together more accurately than at present.     

A practical approach for predicting fatigue reliability under random cyclic loading

The purpose of this paper is to provide a simple approach for reliability analysis based on fatigue or overstress failure modes of mechanical components, and explain how this integrated method carries out spectral fatigue damage and failure reliability analysis. In exploring the ability to predict spectral fatigue life and assess the reliability under a specified dynamics environment, a methodology for reliability assessment and its corresponding fatigue life prediction of mechanical components using a supply-demand interference approach is developed in this paper. Since the methodology couples dynamics analysis and stochastic analysis for fatigue damage and reliability prediction, the conversion of the duty cycle history for the reliability study of an individual component is also presented. Using the proposed methodology, mechanical component reliability can be predicted according to different mission requirements. For an explanation of this methodology, a probabilistic method of deciding the relationship between the allowable stress or fatigue endurance limit and reliability is also presented.     

Mechanical response of metallic honeycomb sandwich panel structures to high-intensity dynamic loading

Explosive tests were performed in air to study the dynamic mechanical response of square honeycomb core sandwich panels made from a super-austenitic stainless steel alloy. Tests were conducted at three levels of impulse load on the sandwich panels and solid plates with the same areal density. Impulse was varied by changing the charge weight of the explosive at a constant standoff distance. At the lowest intensity load, significant front face bending and progressive cell wall buckling were observed at the center of the panel closest to the explosion source. Cell wall buckling and core densification increased as the impulse increased. An air blast simulation code was used to determine the blast loads at the front surfaces of the test panels, and these were used as inputs to finite element calculations of the dynamic response of the sandwich structure. Very good agreement was observed between the finite element model predictions of the sandwich panel front and back face displacements and the experimental observations. The model also captured many of the phenomenological details of the core deformation behavior. The honeycomb sandwich panels suffered significantly smaller back face deflections than solid plates of identical mass even though their design was far from optimal for such an application.     

A nonlinear model of piezoelectric polycrystalline ceramics under quasi-static electromechanical loading

Nonlinear characteristics of tetragonal perovskite type polycrystalline piezoelectric ceramics under electromechanical loading are theoretically simulated using a threedimensional micromechanical model. The model consists of many differently oriented grains which form the bulk material. Uni-axial, quasi-static loading is applied in the simulations. The calculations which are based on a linear constitutive and nonlinear domain switching model are performed at each grain. All grains are assumed to be statistically random oriented at the virgin state.The behavior of piezoelectric ceramics under constant compressive stress which is applied in the same direction of the cyclic electric field is investigated. The macroscopic response of the bulk ceramics to the applied loading is predicted by averaging the response of individual grains. It is assumed that a domain or a microstructure switches if the reduction in potential energy of the polycrystal exceeds a threshold of critical energy per unit volume of the material. Due to intergranular effects domain switching may occur in reality even for those grains, for which the critical energy level is not reached. This effect is modeled by introducing a probability for domain switching as a function of the actual energy level related to the critical energy level. By use of the probability functions, it is possible to model the nonlinearity even in a small electromechanical loading range. The effect of different probability functions, and material parameters are also analysed. The results of simulations have been compared with experimental data from literature.     

Engineering assessment of cracked structures subjected to dynamic loads using fracture mechanics assessment

This paper presents practical guidance on the assessment of cracked structures subjected to dynamic loading. General reviews of fracture behaviour of structures subjected to dynamic loading are presented. A series of finite element (FE) analyses have been carried out to study the effects of dynamic loading on both fracture toughness specimens under rapid loads and cracked connections in steel framed structures under earthquake loads. FE results of submodel analyses of cracked connections are compared with the results from a simplified method. The simplified method can reduce the analysis time enormously and allows design engineers to assess the possibility of connection fractures, or determine approximate values of toughness and defect size requirements for given peak stress and strain level.