Wind Damage Research Articles

Structural performance and fragility assessment of elevated residential buildings during 2017–2018 hurricanes in Texas and Florida

Elevating coastal houses on columns or piles is recognized as an effective technique for reducing the risks of flooding and storm surges. However, recent hurricanes have exposed a potential vulnerability in this approach, as many elevated residential structures sustained significant wind damage even at wind speeds below the current design level. Elevating a structure increases its exposure to stronger winds and leads to potential changes in the wind effects due to the air gap beneath the floor. However, there has been limited research comparing the performance of actual constructed elevated and slab-on-grade residential structures during realistic wind events. To fill this gap, authors utilized publicly available building performance datasets, collected by the Structural Extreme Events Reconnaissance (StEER) Network and others, to extract data on the performance of 851 elevated and 1536 slab-on-grade residential houses impacted by Hurricanes Irma, Harvey, and Michael. Effects of several key parameters were analyzed in terms of the intensity and distribution of the damage experienced by the different components. Furthermore, empirical fragility functions were developed for different roof shapes and cladding materials by combining the estimated wind speed that affected each structure and the assigned damage ratios for the roof and wall claddings. Analysis using the Wilcoxon rank-sum test demonstrated a statistically significant difference in the median wind speeds of various damage states of the components in both elevated and slab-on-grade houses. Additionally, a significant difference was observed in Texas slab-on-grade houses which experienced either no, minor, moderate, or severe damage, compared to their Florida counterparts. Results showed that elevated houses experience more damage than their slab-on-grade counterparts regardless of the roof shape, cladding materials, and construction age. Additionally, results showed that the elevated houses built in Texas exhibit the highest level of vulnerability among the various housing groups studied. Specifically, the percentage of elevated houses in Texas that experienced destroyed damage state surpassed those of slab-on-grade houses in Texas and elevated houses in Florida by 343 % and 166 %, respectively. The paper identified several knowledge gaps, and it emphasized the need for further experimental tests of building components and different building geometries to improve existing risk models.

Methods for kino evaluation and estimates of genetic parameters in Corymbia

Species within the genus Corymbia are regarded as potential alternatives to Eucalyptus. In addition to having superior wood quality, Corymbia spp. are tolerant to most pests, diseases, and abiotic stresses that affecting Eucalyptus plantations, including physiological disorders, water deficit, and wind damage. However, environmental stresses stimulate kino production, which decreases the quality of pulp and sawn wood. This study aimed to develop a method for evaluating kinoand estimate genetic parameters in Corymbia. For this, 16 Corymbia (C. citriodora × C. torelliana) hybrid clones and 5 clones of Eucalyptus were used. Two evaluation methods (M1 and M2) were tested for kino evaluation; M1 consisted of drilling the bark with Pilodyn and M2 consisted of drilling the heartwood with Pilodyn. The following kino parameters were evaluated: exudation incidence, exudate length which flowed over the stem, and exudate weight. Genetic parameters were estimated by a mixed model method (REML/BLUP). The significance of random effects of the statistical model was tested by the likelihood ratio test. Significant clone effects were obtained for all kino parameters, except for exudate length as assessed by M2. Kino parameters determined by M1 exhibited higher heritability and accuracy. Therefore, M1 should be preferred for kino evaluation in Corymbia.

Analysing 23 years of warm-season derechos in France: a climatology and investigation of synoptic and environmental changes

Abstract. Derechos are severe convective storms known for producing widespread damaging winds. While less frequent than in the United States of America (USA), derechos also occur in Europe. The notable European event on 18 August 2022 exhibited gusts exceeding 200 km h−1, spanning 1500 km in 12 h. This study presents a first climatology of warm-season derechos in France, identifying 38 events between 2000 and 2022. Typically associated with a southwesterly mid-level circulation, warm-season derechos in France generally initiate in the afternoon and exhibit peak activity in July, with comparable frequencies in June and August. Predominantly impacting the northeast of France, these events exhibit a maximum observed frequency of 0.65 events per year, on average, within a 200 km by 200 km square region. These characteristics are similar to those observed in Germany, with notable differences seen in the USA, where frequencies can attain significantly higher values. The study also examines synoptic and environmental changes linked with analogues of the 500 hPa geopotential height patterns associated with past warm-season derechos, comparing analogues from a relatively distant past (1950–1980) with a recent period (1992–2022). For most events, a notable increase in convective available potential energy (CAPE) is observed, aligning with trends identified in previous studies for southern Europe. However, no consistent change in 0–6 km vertical wind shear is observed in the recent period. These environmental shifts align with higher near-surface temperatures, altered mid-level atmospheric flow patterns and often increased rainfall. The role of anthropogenic climate change in these changes remains uncertain, given potential influences of natural variability factors such as the El Niño–Southern Oscillation (ENSO) or the Atlantic Multidecadal Oscillation (AMO).

Assessment of large-scale multiple forest disturbance susceptibilities with AutoML framework: an Izmir Regional Forest Directorate case

Disturbances such as forest fires, intense winds, and insect damage exert strong impacts on forest ecosystems by shaping their structure and growth dynamics, with contributions from climate change. Consequently, there is a need for reliable and operational methods to monitor and map these disturbances for the development of suitable management strategies. While susceptibility assessment using machine learning methods has increased, most studies have focused on a single disturbance. Moreover, there has been limited exploration of the use of “Automated Machine Learning (AutoML)” in the literature. In this study, susceptibility assessment for multiple forest disturbances (fires, insect damage, and wind damage) was conducted using the PyCaret AutoML framework in the Izmir Regional Forest Directorate (RFD) in Turkey. The AutoML framework compared 14 machine learning algorithms and ranked the best models based on AUC (area under the curve) values. The extra tree classifier (ET) algorithm was selected for modeling the susceptibility of each disturbance due to its good performance (AUC values > 0.98). The study evaluated susceptibilities for both individual and multiple disturbances, creating a total of four susceptibility maps using fifteen driving factors in the assessment. According to the results, 82.5% of forested areas in the Izmir RFD are susceptible to multiple disturbances at high and very high levels. Additionally, a potential forest disturbances map was created, revealing that 15.6% of forested areas in the Izmir RFD may experience no damage from the disturbances considered, while 54.2% could face damage from all three disturbances. The SHAP (Shapley Additive exPlanations) methodology was applied to evaluate the importance of features on prediction and the nonlinear relationship between explanatory features and susceptibility to disturbance.

Effect of root zone heating on cold tolerance of papaya (Carica papaya L.)

ABSTRACT Low-temperatures during winter are a serious problem in the cultivation of tropical fruit trees in temperate regions. The study investigated whether root zone heating treatments could improve cold injury tolerance in papaya. Leaf water potential was −2.22MPa and leaves wilted in the Control, where the root zone was not heated. However, where the root zone was heated to 20°C or only during the daytime, leaf water potentials were −1.31MPa and −1.41MPa, respectively, and no signs of leaf wilting were observed, suggesting that cold wind damage was suppressed unless temperatures fell below freezing. In contrast, where the root zone was heated, leaves wilted rapidly as temperature fell below the freezing point, and all trees had died by 12 January 2018 (72 days of experiment), suggesting that freezing injury could not be controlled by heating the root zone. It is therefore suggested that in addition to root zone heating, heating the greenhouse only on days when the temperature is below the freezing point would also prevent freezing injury. This has the potential to reduce the total greenhouse heating time by 97%. It also has the potential to reduce fuel costs for overwintering papaya, a tropical fruit tree cultivated in a temperate region.

Damage prediction for planted longleaf pine in extreme winds

Severe wind disturbances are forecast to increase in frequency and intensity with climate change putting forest trees at greater risk of wind damage. Of particular concern are mature and old-growth forests of wind-prone regions which host considerable biodiversity. Landscape configuration, stand structure, and tree characteristics affect susceptibility to wind damage. In managed forests and restoration contexts, these factors could be manipulated to enhance resistance to severe wind events. We measured landscape, stand, and tree characteristics, and damage in longleaf pine (Pinus palustris Mill.) forests in southwest Georgia and Northwest Florida affected by Hurricane Michael (2018) and used these data to model wind damage. We hypothesized that wind damage would increase with wind exposure and decrease with diameter-to-height ratio (taper). We found that lower wind exposure and higher taper resulted in substantially lower wind damage. We conclude that maintaining lower stand density during stand development could reduce wind damage by increasing individual tree resistance to wind. Management and restoration activities that increase resilience to threats from extreme weather can help maintain persistence and landscape restoration of global biodiversity hotspots in wind-prone regions.

Mosses for minimalist green roofs: A preliminary study of the effects of rooftop exposure, species selection, and lab-grown vs. wild-harvested propagule sources

Mosses are rarely explicitly included in urban green infrastructure projects in much of North America. Nevertheless, their opportunistic colonization of impervious surfaces in the absence of intervention, combined with successful tests of their suitability in other parts of the world, suggests that they may be suited to expanded use in applications such as green roofs, and beneficial to urban ecosystem services. Such inclusion requires more detailed knowledge of both general methods for incorporating mosses into green infrastructure, and species-specific knowledge on propagation methods and maximizing growth. In this report, we present a 3-year green roof trial with five types of moss replicated across both wild and lab grown inocula, on both sheltered and exposed asphalt roof surfaces in Atlantic Canada. The exposed roof surface was not conducive to bryophyte survival; repeated wind damage, combined with rapid onset of chlorosis from drought stress, resulted in a complete mortality of all species in that condition. In the sheltered habitat, all species were still present by the third year, but with much lower cover than was present post-installation. In general, wild-harvested shoots survived better than lab-cultivated ones, and those mosses transplanted from shady habitats fared better than those from sunny habitats. We conclude that surface attachment and degree of exposure are the most important factors for establishing moss growth on asphalt roofs, whereas selecting among species may be important only in the context of maximizing long-term growth under highly localized conditions, such as high litter deposition or partial vs. full shade from overhead trees.

A Review on the Status of Rubber Plantations in Cambodia

The rubber tree (natural rubber) is a tropical crop around the world. In Cambodia, rubber is one of the most popular agro-industrial crops introduced since the 1910s. This study review article aims to demonstrate the methods for planting and harvesting techniques in rubber plantations. Cultivation is the most important factor in the rubber sector, and planting is done during June and July. Moreover, selecting varieties of clonal rubber is the best way to improve high production, high initial vigor, tolerance to climate change, pests, wind damage, and diseases, and to be a good secondary characteristic. In addition, harvesting techniques are vital elements in the status of rubber plantations. So, improving the methods of cultivation and the techniques of harvesting is very important in order to get a high amount of rubber production.

Severe storm damage and short‐term weather stresses on corn: A review

AbstractAdverse weather conditions from acute events (e.g., storms causing lodging, flooding, or hail) or short‐duration weather patterns (i.e., periods of cold events; extended waterlogged field conditions) can result in yield losses, though management practices may play key roles in aiding with crop recovery or avoidance of these stress events. This review summarizes current knowledge (with emphasis placed on the US Midwest) related to corn response to short‐term weather stresses of (i) cold temperature, (ii) excess water, (iii) hail/defoliation damage, and (iv) wind damage. Each section presents summaries of how corn growth and yield are affected, provides context into past events experienced, identifies agronomic or production recommendations to correct or alleviate the stress condition, and proposes areas where future research is needed. This review also highlights challenges associated with controlled simulation work on these stressors, and also identifies key areas to expand future research efforts. In general, yield losses associated with strong storms and short‐term weather events often ranged from 5% to 35%, but extreme cases could result in up to 80%–100% yield loss. Much of the literature on these topics was published prior to 1995, though it still forms the basis for modern agronomic guidance, which is problematic given the changes in agriculture in the last 20 years in management practices, available genetics and technologies, and changing environmental conditions. Revisiting these foundational studies and expanding them to examine current and future weather conditions are critical for better informing agronomic recommendations, for devising mitigation strategies, and for determining accurate yield loss expectations following these stresses.

Farmer preference for macadamia varieties and constraints to production in Malawi.

Macadamia nuts constitute a vital component of both nutrition and livelihoods for smallholder producers in Malawi. We conducted a comprehensive mixed-methods study, combining qualitative and quantitative analyses, to explore varietal preferences and production challenges among these farmers. Leveraging cross-sectional data from 144 members of the Highlands Macadamia Cooperative Union Limited, our study underscores several significant findings. Our findings reveal that the majority of smallholder macadamia farmers (62%) are aged over 50, with farming as their primary occupation. Varied preferences are driven by yield-related traits, including high yield potential (38%), nut quality (29%), and extended flowering patterns (15%). Among the macadamia varieties, the top five choices, grown by over half of the farmers, include HAES 660 (18%), 800 (10%), 791 (9%), 816 (8%), and 246 (7%). Additionally, our study identifies five primary constraints faced by smallholder macadamia farmers: insect pests (81%), diseases (34%), limited market access (33%), wind damage (25%), and inadequate agricultural advisory services (17%). Based on these findings, we propose two policy recommendations to enhance smallholder macadamia production and productivity in Malawi and other regions. Specifically, we advocate for informed breeding programs that align with farmer preferences to promote greater adoption of macadamia varieties. Additionally, we emphasize the crucial role of the Malawian government in the macadamia value chain, suggesting active participation in providing extension services and marketing support, akin to its support for other cash crops.

A field investigation to evaluate the effects of prevailing wind and solar radiation on water-induced damage to the eaves of wooden fiber-board covered roofs

Due to various reasons, problematic spots where leakage may occur manifest on the surface of the eave and gutter components of roofs and on the joints between the components. Depending on their characteristics, wind and sunlight are climatic parameters that have a gradual impact in rendering various types of damage at these points. In this article, an observation-based investigation and evaluation was made of the wooden fiberboard-covered eaves of the roofs of a 28-building mass residential settlement in the district of Maslak, Istanbul, and constructed in 2007, to assess the effect of prevailing wind and solar radiation related various damages that had occurred over the 12-year life cycle of the residential complex. The impact ratios according to direction were assessed taking into consideration prevailing wind frequency and solar radiation amount. The results of the evaluation showed that the rupture and divergence defined as destructive damage in the veneer of the wooden fiberboard roof eaves changed in parallel with the forcefulness of the prevailing wind. In the directions where the effect of solar radiation was low, it was seen that due to delayed drying, the planks of wooden fiberboard displayed swelling, mossing, and cracked joints, and also damage in the form of deformations and ruptures.

Preparing for the expected: cyclone threats

The Gold Coast is a bustling region in South East Queensland with a large concentration of people and has dynamic and growing business and tourism activity. The region is subject to thunderstorms and tropical cyclones that can generate damaging winds. The Severe Wind Hazard Assessment for South East Queensland evaluates the risk posed by severe winds and has strategies for managing this risk (Edwards et al. 2022). Results from the most recent assessment showed that older residential houses were the most damaged by severe winds and that this contributed disproportionately to community risk. However, lessons from recent wind damage caused by Tropical Cyclone Seroja in Western Australia in 2021 indicated that modern house designs have important vulnerabilities. These findings are a concern for any exposed coastal area and, in particular, for South East Queensland. This paper presents a suite of scenarios developed to address this vulnerability. Specifically, we describe how emergency and disaster managers can conduct capability analyses with the goal to enhance intelligence and planning capabilities. An example of the City of Gold Coast was used to show how it has leveraged these capabilities to improve emergency risk-based planning and begin a community resilience transformation with effective places of refuge and evacuation centres for the community.

Component-based estimation of recovery time and time-related expenses after hurricane events

Introduction: Due to hurricane damage, building residents or businesses must be relocated during the recovery time, which leads to time-related expenses (TRE), also known as additional living expenses (ALE) or extra expense coverage (EEC) or business interruption insurance (BIC). TRE are difficult to predict since they depend on the damage and time necessary to repair the building as well as on external factors such as damaged utilities and the availability of labor and materials, among other issues.Methods: In this study, we developed a new TRE hurricane vulnerability model for mid/high-rise buildings. The model combines estimates of repair time (Trepair), delay time (Tdelay), and utilities downtime (Tdown) to predict overall recovery time (Treco).Results: The outputs of the model include 1) TRE vulnerability matrices, which yield probabilities of Trepair, Tdelay, Tdown, Treco, and TRE conditional on either maximum 3-s wind speed or overall building damage ratio; 2) the corresponding vulnerability curves, which yield the mean values as a function wind speed or damage ratio.Discussion: Insurers can use these results to project TRE, and emergency managers and urban planners can use the recovery times to characterize the resilience of coastal communities. This paper summarizes the methodology and illustrates its implementation and results. The selected results of Treco are compared with the recovery times provided using the HAZUS-MH Hurricane Model.

Ensemble Bayesian Model Averaging Projections of Wind‐Speed Extremes for Wind Energy Applications Over China Under Climate Change

AbstractWind energy has grown rapidly in recent years as a measure to control carbon emissions and mitigate climate change. Extreme wind can damage wind turbines, cause losses to wind power plants, limit economic benefits of wind energy facilities, and disrupt regional grid balance. Therefore, an accurate assessment of extreme wind speeds at wind turbine hub height and their spatiotemporal variation under climate change is critical for the planning of wind energy and for guaranteeing regional energy security. In this study, the 100‐m extreme wind speeds in China are estimated using an empirical downscaling and Bayesian model averaging ensemble method with the latest ERA5 reanalysis and 20 global climate models (GCMs) from the Coupled Model Intercomparison Project phase 6 (CMIP6). Two shared socioeconomic pathways (SSP), that is, SSP2‐4.5 and SSP5‐8.5, are considered to account for the uncertainty in anthropogenic emissions. According to the results, the highest extreme wind speeds are primarily found in Inner Mongolia, northeast China, western Tibet, and the eastern coastal region. Extreme wind speeds in central and southeastern China are projected to increase by approximately 2% in the middle (2031–2060) and the end (2071–2100) of the 21st century relative to the baseline period (1985–2014). Summer extreme wind speeds in northwestern Tibet are expected to increase by more than 9% at the end of the century. The findings of this study indicate that it is important to take the present and projected changes in local wind extremes into account when choosing locations for wind power plants and wind energy installations.

Measuring 3D tree imbalance of plant models using graph-theoretical approaches

Imbalance in the 3D structure of plants can be an important indicator of insufficient light or nutrient supply, as well as excessive wind, (formerly present) physical barriers, neighbor or storm damage. It can also be a simple means to detect certain illnesses, since some diseases like the apple proliferation disease, an infection with the barley yellow dwarf virus or plant canker can cause abnormal growth, like “witches' brooms” or burls, resulting in a deviating 3D plant architecture. However, quantifying imbalance of plant growth is not an easy task, and it requires a mathematically sound 3D model of plants to which imbalance indices can be applied. Current models of plants are often based on stacked cylinders or voxel matrices and do not allow for measuring the degree of 3D imbalance in the branching structure of the whole plant.On the other hand, various imbalance indices are readily available for so-called graph-theoretical trees and are frequently used in areas like phylogenetics and computer science. While only some basic ideas of these indices can be transferred to the 3D setting, graph-theoretical trees are a logical foundation for 3D plant models that allow for elegant and natural imbalance measures.In this manuscript, our aim is thus threefold: We first present a new graph-theoretical 3D model of plants and discuss desirable properties of imbalance measures in the 3D setting. We then introduce and analyze eight different 3D imbalance indices and their properties. Thirdly, we illustrate all our findings using a data set of 63 bush beans. Moreover, we implemented all our indices in the publicly available R-software package treeDbalance accompanying this manuscript. Using this software package, all presented 3D imbalance indices can be computed in linear time (depending on the size of the 3D plant model), and the package also provides an implementation of the algorithm to obtain a perfectly balanced version of a given 3D plant model (also in linear time).

Investigation on Wind-Induced Structural Damage and Preventive Measures of Low-Rise Buildings in Coastal Areas

Abstract Strong winds, typhoons, and other extreme weather can cause significant damage to house structures, resulting in great harm to human life and property safety. It is imperative to prepare and strengthen infrastructure against these extreme weather conditions to minimize their impact. This paper conducts an on-site survey of low-rise houses in Cangnan County and Dongtou District, located on the south coast of Zhejiang, affected by typhoons. It summarizes the structural characteristics of houses and the damage caused by typhoons to house structures. The paper also performs a preliminary analysis of the damage mechanism of houses. Additionally, it examines wind-resistant measures used by the private sector, identifies potential issues with wind-resistant design, and proposes corresponding wind-resistant countermeasures and recommendations for low-rise houses. The research presented in this paper can be utilized for analyzing the wind damage mechanisms of low-rise houses in the future. Moreover, it offers a valuable reference for the analysis and simulation of wind damage in low-rise houses in typhoon-prone coastal areas. This research holds significant value in preventing wind damage to low-rise houses.

Key traits influencing the resistance of Eucalyptus camaldulensis to wind damage in coastal areas of South China.

China is one of the countries in the world most seriously affected by typhoons, which pose a great threat to the eucalyptus plantation industry. However, few studies have comprehensively accounted for the impact of key traits on the wind damage/resistance of eucalyptus. To identify the key factors affecting the wind resistance of eucalyptus, 20 eucalyptus genotypes were selected; a total of 18 traits, including the wind damage index, growth traits, and wood traits, were measured, and the wind resistance was determined via the tree-pulling test. Correlation, principal component, canonical correlation, and path analyses were performed to evaluate these traits. Correlation analysis revealed that the wind resistance of eucalyptus plants was related to the tree height, volume, and duration of stress wave propagation. Principal components and tree-pulling variables were further used for correlation and path analyses. Canonical correlation analysis and the PA-OV model showed that holocellulose and lignin contents and fiber width, as well as growth traits, were important factors affecting the stability of standing trees under typhoon conditions. The key traits influencing the wind resistance of Eucalyptus camaldulensis, which may provide a reference for evaluating the wind resistance of Eucalyptus varieties for forest management, were identified. This study provides a knowledge base for forest management and planning in typhoon-prone coastal areas, and provides a theoretical basis for the breeding and genetically improving eucalyptus stocks based on wind resistance characteristics.

Integrating wind disturbances into forest planning: a stochastic programming approach

Forest disturbances challenge our ability to carefully plan for sustainable use of forest resources. As forest disturbances are stochastic, we cannot plan for the disturbance at any specific time or location. However, we can prepare for the possibility of a disturbance by integrating its potential intensity range and frequency when developing forest management plans. This study uses stochastic programming to integrate wind intensity (wind speed) and wind event frequency (number of occurrences) into the forest planning process on a small coastal Finnish forest landscape. We used a mechanistic model to quantify the critical wind speed for tree felling, with a Monte Carlo approach to include wind damage and salvage logging into forest management alternatives. We apply a stochastic programming model to explore two objectives: maximizing the expected forest net present value or maximizing the even-flow of income. To assess the effects of improper wind risk assumptions in planning, we compare the results when optimizing for correct versus incorrect wind intensity and frequency assumptions. When maximizing for net present value, the impacts of misidentifying wind intensity and frequency are minor, likely due to harvests planned immediately as trees reach maturity. For the case when maximizing even-flow of income, incorrectly identifying wind intensity and frequency severely impacts the ability to meet the required harvest targets and reduces the expected net present value. The specific utility of risk mitigation therefore depends on the planning problem. Overall, we show that incorporating wind disturbances into forest planning can inform forest owners about how they can manage wind risk based on their specific risk preferences.

A model to predict maximum tangential wind velocity in laboratory-scale fire whirls without flames in a crosswind

Fire whirls cause strong wind damage in large outdoor fires such as wildland fires and urban fires. A model to predict the maximum tangential wind velocity in laboratory-scale fire whirls without flames in a crosswind is developed based on a generation mechanism and the properties of the fire whirls. The model also predicts the radii of the fire whirls and the crosswind speed when they occur. The fire whirls modeled are those with large circulation and large radii, that is, large intense fire whirls. These fire whirls occur and remain downwind of a fire line placed perpendicular to the crosswind under a low crosswind speed and a high heat release rate (HRR). The model agrees well with the experimental results.

Experimental Study on Static Wind Uplift Resistance of Roofing Systems

Metal roof systems were widely utilized in various important buildings; however, cases of wind damage were often observed. In this paper, wind uplift tests of standing seam aluminum magnesium manganese and continuous welded stainless-steel roof systems were conducted, and the wind resistance bearing capacity and mechanical properties of key joints in the two roof systems were compared and analyzed. Strain gauges and displacement sensors were arranged at different structural layers and key nodes of the roof system to compare and analyze the stress and displacement changes. The results showed that the wind resistance capacity of the continuous welded stainless-steel roof system was more than 25% higher than that of the standing seam aluminum magnesium manganese roof system. The stress and displacement of the roof system gradually increased with the increase in wind load. Obvious differences in stress at different positions of the two roof systems were identified. The stress at the roof panel of the roof system was greater than that of other structural layers, and the maximum displacement of the roof panel in the elastic stage could reach more than 97.5 mm. The fitting coefficient between the test and the finite element was 0.976, and the ultimate bearing capacity of Specimen B was 479.64 MPa. The research results of this paper can provide some data support and reference for engineering design and applications.