ANSYS Software Research Articles

CFD analysis of key factors impacting the aerodynamic performance of the S830 wind turbine airfoil

The Global Wind Energy Council (GWEC) reported that in 2021, global wind capacity increased by 93.6 GW (+12%), reaching a total of 837 GW, most of which was contributed by wind turbines. Improving wind turbine performance primarily hinges on advancements in blade technology and airfoil design. This study examines the effect of profile thickness on the aerodynamic performance of the S830 airfoil at a Reynolds number of 25,148, as part of the NREL airfoil's aerodynamic performance research. However, the impacts of additional variables—such as angle of attack, Reynolds number, speed range, and particularly ice accretion—have not been thoroughly investigated. This study utilized a 2D CFD model provided by the commercial software ANSYS Fluent and FENSAP-ICE. The lift-to-drag ratio of the S830 wind turbine airfoil was examined, considering the effects of angle of attack, wind speed, Reynolds number, airfoil thickness, and ice accretion. Additionally, design-related solutions will be suggested. The research indicates that the optimal angle of attack increases the lift-to-drag ratio by approximately 250% compared to a zero angle of attack. An increase in wind speed causes this coefficient to rise nonlinearly within the studied velocity range. The Reynolds number directly influences the optimal angle of attack. According to CFD results, the lift-to-drag ratio can be increased by 50% if the airfoil's thickness is reduced by 20% compared to the original profile. For the ice accretion simulation model, a case test of the NACA 0012 airfoil was conducted to verify the model's parameters. Subsequently, a survey of this phenomenon on the S830 airfoil revealed that the lift coefficient decreased by 5.25% after 90 minutes of ice accretion.

Computational fluid dynamics analysis of flat plate type solar collector under different fin variables to enhance air-based heat transfer

Purpose This study begins by outlining the core principles of how flat plate solar collectors (FPSC) operate and the underlying mechanisms of heat transfer. It underscores the pivotal role of fin patterns in enhancing convective heat transfer. Design/methodology/approach The primary objective is to examine the impact of diverse fin patterns on the thermal performance of FPSCs. The study involves the development of a 3D-CFD model for FPSC using the computational fluid dynamics (CFD) software ANSYS FLUENT. The analysis is conducted for variable mass flow rates (mf) ranging from 0.01 to 0.05 kg/s with an interval of 0.02 kg/s. Each flow rate is assessed for three distinct fin patterns: straight plate fins, V-shaped fins and wavy fins. Recognizing the variation in solar radiation intensity throughout the day, the analysis is executed at six different time points ranging 10:00 a.m. to 03.00 p.m. with a time interval of 1.00 h. Findings It is observed that the wavy fin pattern with a mass flow rate of 0.01 kg/s exhibited the highest outlet temperature, showing a significant temperature difference of 12.4 K at noon. Conversely, the V-shaped fin pattern with a mf of 0.05 kg/s has the lowest temperature difference value, measuring only 3 K. The analysis included the calculation of thermal efficiency for each case, revealing that the V-shaped fin pattern at a mf of 0.05 kg/s and a sun radiation intensity of 885.42 W/m2 achieved the maximum instantaneous thermal efficiency (ηth) of 34.7%. The study records the outlet air temperature for all of these combinations and presents the data graphically in the paper. Originality/value The findings of the simulations indicate that the thermal performance that is ηth and maximum temperature of outlet air of FPSCs can be improved through the utilization of variable fin patterns.

Design and Simulation Study of Structural Parameters of Bionic Cutters for Tea Harvest Imitating Aeolesthes induta Newman

The cutter of the hand-held tea picker is the key cutting component in the efficient tea harvesting process. In order to solve the problems of large cutting resistance and uneven incision during tea picking, this study fully applied the bionics principle to combine the excellent cutting performance of Aeolesthes induta Newman’s mandibles with the tea cutter, which extracted and fitted the tooth profile structure curve of the upper edge of the Aeolesthes induta Newman’s mandibles. The trapezoidal teeth on the reciprocating cutter of ordinary hand-held tea-picking harvesters were optimized by the fitted curve, and a new tea cutter with the shape of Aeolesthes induta Newman teeth was obtained, which included four kinds of bionic tea-harvesting cutters. The multi-body system software ADAMS 2020 and finite element analysis software ANSYS 2024R1 were used to compare the kinematics, statics and explicit dynamics of cutting properties of the four bionic cutters and common cutters with ordinary trapezoidal teeth and saw teeth. The simulation results showed that the maximum equivalent elastic strain and the maximum cutting force during the cutting operation were reduced by 36.7% and 42.89%, respectively, for the cutting teeth of the bionic tea-harvesting cutter #4 compared with that of the cutter with ordinary trapezoidal teeth. The bionic tea-harvesting cutter designed in this study has better cutting performance than the cutter with traditional cutting teeth, which can effectively reduce the cutting force and improve the flatness and cutting quality of the cutting surface.

Numerical Optimization of Functionally Graded Ti-HAP Material for Tibial Bone Fixation System

Functionally graded materials (FGMs) are heterogeneous composites characterized by outstanding properties. They are built from two or more components with a gradient distribution of chemical composition along a given direction. A promising graded material for biomedical engineering as an implant could be a FGM made of titanium (Ti) and hydroxyapatite (HAP). It would allow us to counteract the difference between the stiffness modulus of pure titanium and bone tissue. Moreover, it can be a good solution to the problem of stress shielding for bone fixation plates made of conventional titanium or steel. The presented paper aims to perform micromechanical modeling and optimization of a functionally Ti-HAP graded plate, followed by numerical analysis of a fractured tibia stabilization system under specific boundary conditions. Finite element analysis was performed using ANSYS Workbench 2021 software. The models of the FGM plate and tibial fixation system were made using the Space Claim tool. The ANSYS software allowed the optimization of the model considered and the selection of the appropriate structural parameters of the FGM Ti-HAP material. In general, the results proved that the osteosynthesis plate built of graded Ti-HAP material resulted in lower bone stress compared to titanium and steel plates. The results obtained confirmed the validity of the design and the possibility to use functionally graded Ti-HAP bone fixation plates.

Numerical and geometric investigation of pool boiling heat transfer in cavities with isothermal rectangular corrugations

This numerical work presents a geometrical investigation of a corrugated isothermal surface placed in a two-dimensional cavity subjected to unsteady, turbulent pool boiling flows. The main purposes are maximizing the heat transfer rate between the isothermal surface and the surrounding water flow, and the volume of vapor generated into the cavity. The geometric investigation followed the constructal design method, being the ratio Hi/Li (i = 1, 2 or 3) of the corrugations varied for three different numbers of corrugations: N = 1, 2, and 3, keeping constant the corrugations area. The volume of fluid (VOF) and Lee's evaporation-condensation models are used to estimate the volume fractions of water vapor/liquid and interfacial mass transfer. The unsteady Reynolds Averaged Navier Stokes (URANS) continuity, momentum and conservation of energy equations, and volume fraction transport equation, are solved using the finite volume method (FVM) available in software Ansys FLUENT. For closure of turbulence, the k - ɛ model is adopted. For validation of the model, the heat flux and convection heat transfer coefficient obtained for a pool boiling bared surface case are compared with Rohsenow's correlations, and differences lower than 7.0 % are reached. Results indicated a strong influence of the ratio Hi/Li and number of corrugations (N) in the heat transfer rate per unit depth (qs) and dimensionless volume of vapor (Vdim) generated into the cavity. The highest intrusion of the corrugations led to the generation of few large and many small scales, benefiting the thermal performance, regardless of the performance indicator employed. The optimal configuration, N = 3 and H3/L3 = 2.0 improved 49 % and 188 % the Vdim and qs compared with the worst corrugated case, showing the importance of the geometry of the corrugation in this problem.

Effect of Soil-Structure Interaction on A Building Frame with Shear Walls

The soil conditions highly influence the damage to structures throughout earthquakes. Hence the research on the energy transfer mechanism from soils to buildings during earthquakes is demanding area of study for the high-rise buildings. For the current study, reinforced concrete frames of G+15 stories with shear walls in the buildings were modeled using ANSYS software. The effect of soil-structure interactions was considered as well. Transient analysis was performed on the three-dimensional frames with shear walls subjected to seismic loading were gauged for the contrast in natural frequency, base shear, roof deflection and Storey drifts. The analysis of results indicates that the behaviour of the structure is very much dependent on the natural frequency of the structure.

Comparative Analysis of Boron-Al Metal Matix Composite and Aluminum Alloy in Enhancing Dynamic Performance of Vertical-Axis Wind Turbine

This study aims to assess the dynamic performance of the vertical-axis wind turbine (VAWT) with the help of conventional aluminum (Al) and the boron Al metal matrix composite (MMC). The simulations were conducted using ANSYS software and involved natural frequencies, mode shapes, a mass participation factor, and Campbell plots. The results of static structural analysis show that the boron Al MMC is vastly superior to the aluminum alloy because there is a 65% reduction of equivalent stress with a 70% reduction of deformation compared to the aluminum alloy. These results show that boron Al MMC can withstand higher loads with lesser stress; the structure remains compact and rigid in its working conditions. From the findings, it can be ascertained that employing boron Al MMC improves VAWT power, efficiency, and robustness. However, the critical speed that was established in the dynamic analysis of boron Al MMC requires extraordinary control and the use of dampening systems, thereby avoiding resonance. Overall, boron Al MMC contributes to significant enhancements in the VAWTs’ mechanical and operational characteristics; however, the material’s complete potential can be achieved only with proper maintenance and employing the correct damping techniques. Information about these two materials will allow for a better understanding of their comparative efficacy and their potential application in the further development of VAWTs.

Study on Atomization Mechanism of Oil Injection Lubrication for Rolling Bearing Based on Stratified Method

The atomization mechanism of lubrication fluid in rolling bearings under high-speed airflow between the rings was investigated. A simulation model of gas–liquid two-phase flow in angular contact ball bearings was developed, and the jet lubrication process between the bearing rings was simulated using FLUENT computational fluid dynamics software (Ansys 19.2). The complex motion boundary conditions of the rolling elements were addressed through a layered approach. We can obtain more accurate boundary layer flow field changes and statistics of the diameter of oil particles in lubricating oil atomization, which lays the foundation for analyzing the law of influence on lubricating oil atomization. The results show that as the number of boundary layer layers increases, the influence of the boundary layer flow field on the lubricating oil is more obvious. The oil particle size is excessively flat, and the concentration of large particles of oil appears to decrease. As the speed increases, the amount of oil in the cavity decreases, but the oil droplets are also fragmented, which intensifies the atomization and reduces the particle diameter. This reduces the Sauter Mean Diameter (SMD), which is not conducive to the lubrication of the bearing. Under different injection pressures, when the injection pressure is large, it is beneficial to the lubrication of the bearing.

Simulation analysis of force and fatigue life of circular wheel of crawler vehicle

During loading and driving, the wheels bear the vertical load from the body mass and the excitation load generated by uneven road surface on the one hand, and bear the driving torque on the other hand. The load-bearing methods of wheels are generally divided into bottom load-bearing and top load-bearing. This paper describes the structural characteristics of the track system of the articulated track vehicle and the interaction relationship between the main components of the track system. Finite element calculation is carried out based on ANSYS software to obtain the stress distribution of each key component under various loading methods. It can be seen from the results that all key components of the track system can meet the strength and rigidity requirements; although there are also areas with large local stress, they are all within the safe range, which is mainly caused by stress concentration. Safe life is obtained through fatigue analysis.

Reliable comparison of multi-directional mechanical properties for biomimetic circle arc honeycombs

Abstract Compared to straight honeycombs, curved honeycombs derived from biomimetic strategies typically exhibit superior mechanical properties and a broader tunable range. Consequently, there has been a surge in research focusing on curved honeycombs. However, few studies have concurrently designed multiple honeycombs for reliable comparisons, and little attention has been given to isotropy. In this study, circle arc walls were introduced to replace the straight walls of five classical honeycombs, thereby creating representative curved honeycombs for analysis. The numerical modeling method in ANSYS software was validated by experimentally testing 3D printed specimens of circle arc honeycombs. At the same mass and under loading conditions in different directions, it was found that the Young's modulus, yield strength, Poisson's ratio, and energy absorption of circle arc hexagon (CAH), circle arc square (CAS), circle arc triangle (CAT), circle arc re-entrant (CAR), and circle arc double-V (CAD) were assessed. Both experimental and numerical results revealed that CAH demonstrates superior energy absorption while maintaining a high degree of isotropy, characterized by all isotropic factors below 0.1 in mechanical properties. Notably, CAD exhibits a Negative Poisson's ratio (NPR) effect across all loading directions. These results provide benchmarks for future studies on curved honeycombs and guide further research in this field.

Effect of Thermal Load Caused by Tread Braking on Crack Propagation in Railway Wheels on Long Downhill Ramps

To investigate the propagation behavior of thermal cracks on the wheel tread under the conditions of long downhill ramps, a three-dimensional finite element model of a 1/16 wheel, including an initial thermal crack, was developed using the finite element software ANSYS 17.0. The loading scenarios considered include mechanical wheel–rail loads, both with and without the superposition of thermal wheel–brake shoe friction loads. The virtual crack closure method (VCCM) is employed to analyze the variations in stress intensity factors (SIFs) for Modes I, II, and III (KI, KII, and KIII) at the 0°, mid, and 90° positions along the crack tip. The simulation results show that temperature is a critical factor for the propagation of thermal cracks. Among the SIFs, KII (Mode II) is larger than KI (Mode I) and KIII (Mode III). Specifically, the thermal load on the wheel tread during braking contributes up to 23.83% to KII when the wheel tread reaches the martensitic phase transition temperature due to brake failure. These results are consistent with the observed radial propagation of thermal cracks in wheel treads under operational conditions.

Numerical characterizations of the thermomechanical response of power modules with ceramic substrates and lead-free bonds

PurposeThe present paper aims to study the influence of the substrate system on the thermomechanical response of various lead-free die attach materials used in power electronics using nonlinear finite element simulations.Design/methodology/approachParticularly, three ceramic substrate systems, including direct copper bonded (DCB) and aluminum nitride (AlN) – as well as silicon nitride (Si3N4) –based insulated metal substrate (IMS) configurations are examined in this study. Additionally, three die attach systems, namely, silver-tin transient liquid phase (TLP), sintered silver (Ag) and sintered copper (Cu) are included in the analysis. ANSYS software is employed to build the finite element models of the power modules and to conduct the nonlinear thermomechanical investigations.FindingsThe simulation results revealed that the IMS, Si3N4 and DCB-based power modules end up with significantly lower interconnect inelastic strains and inelastic strain energies suggesting better fatigue life performance. Additionally, the bonding layer stresses and expected failure mechanism are not influenced by the substrate configuration rather than the bond material. For instance, the silver-tin TLP joints develop high stresses and hence brittle failures are expected. Nonetheless, the sintered Ag and sintered Cu have significantly lower stresses which could lead to fatigue-induced failures.Originality/valuePower electronics use various ceramic-based substrate systems because of their improved thermal conductivity, electrical insulation and heat resistance properties. The proper selection of the substrate structure could highly enhance the thermal fatigue of the power modules. Markedly, the findings of this research are useful for designing highly reliable and effective power modules continuously subjected to thermomechanical loadings.

Modeling the Geometry and Filter Composite of the Air Cleaner.

Air pollution is currently the most significant environmental factor posing a threat to the health and lives of European residents. It is a key cause of poor health, particularly respiratory and cardiovascular diseases. The primary aim of the study was to numerically determine the impact of the air purifier model's geometry on the distribution of air within a room and to conduct experimental tests on the filtration efficiency and preliminary antibacterial activity of filtration composites. The scope of the work included designing an air purifier model in the form of a pendant lamp and performing computer simulations in Ansys software to identify the optimal shape. The experimental research focused on developing filtration composites consisting of nonwoven fabric with an active hydrosol layer, meltblown nonwovens and a carbon filter. The study results showed that the SMMS composite with 50% thyme and carbon nonwoven exhibited the highest filtration efficiency for both small and large particles.

Using the Finite Element Simulation Software Ansys to Analyze the Stress and Strain Generated in the Eyeball due to Pressure When Subjected to Compression

Using the Finite Element Simulation Software Ansys to Analyze the Stress and Strain Generated in the Eyeball due to Pressure When Subjected to Compression

Dynamic Modeling and Analysis of Multi-Span Timoshenko Beams Under Moving Loads

Dynamic response analysis of multi-span beams is one of the important topics in the field of highway and railway engineering, which provides valuable guidance for the design, operation and maintenance of multi-span bridges. It is worth considering how to calculate the dynamic characteristics of multi-span beams quickly and conveniently. In this study, an effective analytical method is developed for the dynamic modeling and investigations of multi-span Timoshenko beams under moving loads by employing the assumed mode method (AMM). Based on Hamilton’s principle, the equation of motion of the Timoshenko multi-span beam subjected to moving loads is formulated and the natural frequencies are calculated. A comprehensive investigation is conducted on the dynamic responses of the multi-span Timoshenko beam considering different factors, including the length-to-thickness ratio, disorder degree, arrangement order, number of spans and related parameters of moving loads. In addition, the influence of the interval and velocity of the moving load series on the dynamic responses, including displacement, velocity and acceleration of the multi-span beam, are analyzed in detail. The theoretical calculation results of multi-span Timoshenko beams under moving loads are compared with numerical results obtained from ANSYS software, and the results are in good agreement. This demonstrates that the developed method, which utilizes the AMM to analyze the dynamic characteristics of multi-span beams subjected to moving loads, significantly simplifies the calculations and is well-suited for practical engineering applications.

АНАЛІЗ ХАРАКТЕРИСТИК ЛОКАЛЬНОГО НАПРУЖЕНО-ДЕФОРМОВАНОГО СТАНУ З'ЄДНАННЯ МЕТАЛЕВОГО КОМЛЯ З КОМПОЗИТНОЮ ЛОПАТТЮ ПОВІТРЯНОГО ГВИНТА

The article discusses the possibility of modeling the stress-strain state (SSS) of the connection of the metal butt with the composite cylindrical part of the blade using the specialized ANSYS software application and its Composite PrepPost module. Created connection models in ANSYS environment. The optimal designs for connecting the metal butt and composite material have been determined. For a simplified calculation of the connection strength, only the influence of the centrifugal force arising during operation of the screw is taken into account. In the ANSYS software package, a static load of the connection was carried out, which makes it possible to evaluate the nature of the stress distribution in the connection. A butt model and a finite element connection mesh were created. For the calculation, the characteristics of the materials of the blade elements are given. To determine a rational structural-power connection scheme, varying parameters were selected: the number of rows of spikes along the radius, the number of spike belts and the arrangement of the butt spikes. The dependence of the voltage in the composite part of the connection on the arrangement of the butt spikes was obtained. The shape and length of the spike were analyzed. The dependence of voltage on the radius of curvature of the tenon was obtained. The stress-strain state of a tenon-rounded flange is shown in ANSYS. The dependences of voltage on the length of the spike were obtained. The calculation showed that the length of the tenon L has a significant effect on the strength characteristics of the connection between the flange and the composite layer. To determine the rational position of the stud, a calculation was carried out in the ANSYS environment with a shift of all rows of studs by the amount K from the extreme position in engagement with the composite layer and a change in the linear order of the studs to a staggered one. The results of the calculation in the ANSYS environment are presented as a dependence of stress on the displacement K. A flange model is presented, where the stud arrangement is staggered, and the result of the stress calculation in the ANSYS environment. The calculation showed that changing the order of the studs from linear to staggered reduces the maximum stress to 385 MPa. The hydraulic pressure tests confirmed the calculation results. The simulation results showed a significant improvement in the mechanical performance of the joints with minimal design costs.

Mechanical, Fracture, and Thermal Characterization of Post-Cured Hybrid Epoxy Nanocomposites Reinforced with Graphene Nanoplatelets and h-Boron Nitride

The post-curing process of cured composites is essential in enhancing the strength, stiffness, elevating the glass transition temperature, and reducing residual stress in polymer thermoset composites. The curing temperature and time are the key factors that affect these properties. In-situ polymerization method was used to prepare composites with varying weight percentages of graphene nanoplatelets (GNP) and hexagonal boron nitride (h-BN) nanofillers (0.1, 0.2, and 0.3 wt% GNP-based composites; 0.3, 0.4, and 0.5 wt% h-BN-based composites; 0.4, 0.5, and 0.6 wt% h-BN+GNP-based composites). The cured composites were post-cured at temperatures of 80°C, 120°C, and 160°C for 120 minutes in a hot air oven. The presence of GNPs and h-BNs in the composites is confirmed using Raman spectroscopy, Fourier transform infrared spectroscopy (FTIR) and Scanning Electron Microscopy (SEM). Further mechanical and thermal properties were evaluated by conducting tensile, flexural, impact, fracture and differential scanning thermometry (DSC) tests. The simulation analyses were performed using Ansys software, and the results demonstrated a strong correlation with the experimental data, with discrepancies between the two consistently within a standard margin of 20%.

Electric field simulation, structure and properties of nanofiber- coated yarn prepared by multi-needle water bath electrospinning.

To address the issue of low yield in the preparation of nanofiber materials using single-needle electrospinning technology, multi-needle electrospinning technology has emerged as a crucial solution for mass production. However, the mutual interference of multiple electric fields between the needles can cause significant randomness in the morphology of the produced nanofibers. To better predict the influence of electric field distribution on nanofiber morphology, simulation analysis of the multi-needle arrangement was conducted using finite element analysis software. Nanofiber-coated yarn was produced continuously with the core yarn rotating. The water bath was utilized as the receiver of nanofibers on self-made water bath electrospinning equipment. The electric field distribution and mutual interference under seven different needle arrangements was simulated and analyzed by finite element analysis software ANSYS Maxwell. The results indicated that when the needles were arranged diagonally in a staggered pattern and directly above the core yarn, the simulated electric field distribution was relatively uniform, with less mutual interference. The produced nanofibers exhibited a finer diameter and the diameter distribution was more concentrated. In addition, the nanofiber coating showed higher crystallinity and better mechanical properties.&#xD.

Deformation Heat in Tension of Steel Elements

The purpose of the work is an approximate computational and experimental assessment of the specific energy intensity and heat generation at various stages of the material’s operation when the sample is stretched. The paper discusses an approximate method for estimating the specific energy intensity and heat generation at four stages of tensile deformation of a steel sample. Finite element modeling of the work of the manufactured sample under elastic-plastic tension was performed in the ANSYS multifunctional software package. The load in the digital model of the sample was applied according to the full-scale test program. The experiment used flat samples in accordance with GOST 1497, a WAW-1000 testing machine with a 100T microcomputer, and a testo 875i thermal imager with a temperature sensitivity of 0.05 °C at 30 °C. We compared the obtained values on graphs of full-scale tests and a digital model of the samples, identifying critical points and deviation values. Phased loading revealed that the development of destruction occurs on the descending branches and is accompanied by the gradual development of local instability of plastic deformation in the form of a “neck”. It is shown that the heating temperature of the tensile metal can be calculated using the formulas proposed in the paper or by calculation using the ANSYS software package. The test results showed that the surface temperatures of the samples at each stage differ significantly. Four main areas were identified on the graph of changes in the sample surface temperature at a point. An analysis of the existing database of measuring instruments and the ability to obtain and process data was carried out. Experimental values of surface temperatures during continuous quasi-static deformation exceed their calculated values (up to 5 times). The kinetics of changes in the temperature field of the sample surface was carried out using thermographic instruments.

Study on the Susceptibility of Steel Arches with Letting Pressure Nodes Based on Incremental Dynamic Analysis

When soft rock tunnels pass through fractured fault zones, they are particularly susceptible to extrusion and large-scale deformations, especially during seismic events. To address these challenges, this study introduces an innovative yield-support steel arch design featuring a circumferential letting pressure node at its core. This design delivers incremental support resistance within the deformation zone and a susceptibility curve is applied to evaluate the damage probability of the steel arch with a letting pressure node under seismic loading conditions. Measurements of the surrounding rock pressure and structural forces on the steel arch with the letting pressure node were conducted at the Baoshan Jewel Mountain Tunnel in China. The field experiment results revealed a 23% reduction in the surrounding rock pressure and an 11% decrease in the internal forces of the support structure. These findings demonstrate the successful application of the letting pressure node-supported steel arch in mitigating large deformations in soft rock environments. Additionally, using finite element software ANSYS 2022, a seismic time-history analysis was conducted, employing the relative deformation rate of the letting pressure node steel arch as the damage index and the peak ground acceleration (PGA) as the strength parameter to generate the incremental dynamic analysis (IDA) curve. According to the susceptibility curve derived from the incremental dynamic analysis, at the design ground motion level of 8 degrees, the letting pressure node steel arch has a 94% probability of exceeding its normal service life limit and experiencing damage. The findings of this study offer a novel approach to addressing large deformations in soft rock tunnels. The proposed susceptibility curves for steel arches with letting pressure nodes provide a robust foundation for predicting the damage probability of yielding support structures under seismic conditions.