Article
Geosciences, Multidisciplinary
Longlong Chen, Wengang Zhang, Fuyong Chen, Dongming Gu, Lin Wang, Zhenyu Wang
Summary: Anisotropic spatial variability of soil properties has a significant influence on slope failure probability and failure characteristics. The directional angles of scales of fluctuation and the cross-correlation between soil properties are the key factors. General anisotropic spatial variability has a stronger effect on slope reliability compared to transverse anisotropic spatial variability.
GEOSCIENCE FRONTIERS
(2022)
Article
Engineering, Geological
Chao Zhao, Wenping Gong, Tianzheng Li, C. Hsein Juang, Huiming Tang, Hui Wang
Summary: Accurate characterization of subsurface stratigraphic configuration is crucial to geotechnical engineering work, but uncertainty can be significant due to complexity and limited data availability. This paper presents a method for characterizing subsurface stratigraphy with limited borehole data, demonstrating its effectiveness and advantages through comparative analyses and a case study in Western Australia.
ENGINEERING GEOLOGY
(2021)
Article
Green & Sustainable Science & Technology
Jian Wang, Xiang Gao, Zhili Sun
Summary: The paper introduces a method called multilevel Monte Carlo (MLMC) for time-variant reliability analysis, aiming to enhance computational efficiency while maintaining accuracy and robustness. By discretizing the time interval using a geometric sequence of different timesteps and estimating the cumulative probability of failure with corrections from all levels, the method optimizes the number of random samples at each level to minimize computational complexity. Independently computed corrections at each level allow achieving accuracy at a lower cost compared to crude Monte Carlo simulation, while maintaining robustness to nonlinearity and dimensions.
Article
Engineering, Multidisciplinary
Sergio A. Carvajal, Andres F. Medina, Andres J. Bohorquez, Ciro A. Sanchez
Summary: The paper presents an approach that combines Bayesian inference and experimental data to determine the calibration intervals of instruments. This method is suitable for small sample sizes and allows for better utilization of previous knowledge about instrument performance compared to other methodologies.
Article
Engineering, Civil
Wei Zhang, Xiang Liu, Yiqun Huang, Ming-Na Tong
Summary: The durability problem of reinforced concrete structures is significant in civil engineering due to the tendency of steel rebars to rust. Fiber-reinforced polymer (FRP) rebars have emerged as a substitute for reinforcement due to their corrosion resistance, lightweight, and easy construction. However, the low elastic modulus and brittle failure nature of FRP rebars lead to large deflections and cracks in FRP concrete beams without obvious warning signs. The hybrid reinforced concrete beam, which combines the advantages of steel rebars and FRP rebars, is a promising structural form. Hence, reliability analysis is essential to ensure the safety of these hybrid reinforced beams.
ARCHIVES OF CIVIL AND MECHANICAL ENGINEERING
(2022)
Article
Thermodynamics
Ali Akbar Abdoos, Hatef Abdoos, Javad Kazemitabar, Mohammad Mehdi Mobashsher, Hooman Khaloo
Summary: This article presents a probabilistic intelligent method for wind power prediction to minimize the risk caused by the uncertainty of the generated power. The method includes analyzing wind power time series signals, creating training patterns, training patterns using machine learning, and making probabilistic predictions based on Monte-Carlo simulation. The results show that the method accurately predicts wind power generation in 10-minute intervals and can be effectively applied to both deterministic and probabilistic predictions.
Article
Engineering, Electrical & Electronic
Heitor M. Rodrigues Junior, Igor D. Melo, Erivelton G. Nepomuceno
Summary: This paper proposes a novel methodology to determine interval results for power system load flow in three-phase unbalanced distribution networks. The proposed approach incorporates interval arithmetic and the Krawczyk operator to provide reliable interval three-phase results. The effectiveness of the method is demonstrated through computational simulations and its advantages over other methods are proven.
INTERNATIONAL JOURNAL OF ELECTRICAL POWER & ENERGY SYSTEMS
(2022)
Article
Engineering, Geological
Ranjan Kumar, Arka Jyoti Das, Prabhat Kumar Mandal, Rana Bhattacharjee, Subhashish Tewari
Summary: This paper presents a probabilistic approach to analyze the stability of coal pillars considering stable and failed cases in Indian coalfields. By fitting probability distributions and conducting Monte Carlo simulations, the stability of pillars is assessed and failure probabilities are estimated.
INTERNATIONAL JOURNAL OF ROCK MECHANICS AND MINING SCIENCES
(2021)
Article
Mathematics, Applied
H. de la Cruz
Summary: This paper proposes a new numerical simulation method for the probabilistic response analysis of nonlinear random vibration problems. The method has a simplified implementation process and efficient long-term simulation performance.
APPLIED NUMERICAL MATHEMATICS
(2023)
Article
Engineering, Multidisciplinary
Nima Noii, Amirreza Khodadadian, Fadi Aldakheel
Summary: This work proposes a probabilistic approach to phase-field brittle and ductile fracture, considering random material and geometric properties. The macroscopic failure mechanics assumes homogeneity and determinism in materials properties and spatial quantities, while the lower scale with strong fluctuation in properties is approximated with uncertainty. The proposed model employs representative volume elements with random distribution of inclusions and voids to model the uncertainty. Monte Carlo Finite Element Method is used to solve the stochastic PDE-based model and approximate the expected value and variance of the solution field. The model is effective for predicting failure mechanisms in brittle/ductile fracture.
COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING
(2022)
Article
Mechanics
Haibing Peng
Summary: Despite the widespread use of Navier-Stokes equations in computational-fluid-dynamics (CFD), there are still unanswered questions due to the absence of considering the statistical nature of discrete air molecules. In this study, we propose a statistical mechanics-based approach called the volume-element method, which allows for the numerical evaluation of aerodynamic lift and drag. We obtained pressure and friction values as a function of the angle of attack for flat-plate airfoils, and this method can be directly applied to convex-shape airfoils and combined with Monte Carlo simulations for concave-shape airfoils. This approach not only has implications for aerodynamic applications, but also opens up possibilities for further applications in Boson or Fermi gases.
Article
Energy & Fuels
Babak Jamhiri, Yongfu Xu, Mahdi Shadabfar, Fazal E. Jalal
Summary: The prediction of thermal crack propagation in desiccated soils is imperfect. To address this issue, a probabilistic framework is developed to enhance the crack estimation reliability. The results show that cracking probability is imminent in near-surface layers.
GEOMECHANICS FOR ENERGY AND THE ENVIRONMENT
(2023)
Article
Mechanics
Sai-Sai Guo, Jian-Guo Gong, Peng Zhao, Fu-Zhen Xuan
Summary: Current creep life assessment methods for components at high temperatures are primarily based on deterministic analysis, which cannot achieve probabilistic evaluation of creep failure. Therefore, a probabilistic framework for creep life assessment of components at high temperatures was provided. A method of determining the distribution characteristics of material parameters was proposed through random selection of results at each stress level. Monte Carlo simulation combined with finite element analysis technology was used to capture the distribution characteristic of creep rupture life of a typical structural component. The effect of standard deviation of material parameters on creep reliability assessment was discussed. Comparisons between probabilistic and deterministic creep design methods were made. Results showed that the probabilistic analysis strategy can calculate the specific value of failure probability at various loading conditions, instead of two failure probability values (i.e. 100% and 0%) as determined by deterministic analysis. The effect of standard deviation on the mean values of effective stress and creep rupture life of the component depends on the distribution characteristics of material parameters and related variables. A smaller standard deviation reduces the data scatter of effective stress and creep rupture life of the component.
ENGINEERING FRACTURE MECHANICS
(2023)
Article
Engineering, Industrial
Francesco Di Maio, Chiara Pettorossi, Enrico Zio
Summary: The reliability of critical infrastructures, such as power distribution networks, is crucial for modern societies. However, assessing the reliability of such complex systems can be challenging due to their size, complexity, and rarity of failure events. This paper proposes a novel approach that combines survival signature and Monte Carlo simulation to approximate the reliability of a system, thus saving computational cost.
RELIABILITY ENGINEERING & SYSTEM SAFETY
(2023)
Article
Engineering, Geological
Bin Li, Lianyu Zhang, Jinquan Yuan
Summary: This paper proposes a reliability-based design approach that is simple and efficient from a quantile value perspective. The proposed method eliminates the need for repetitive trial and error procedures and only requires a single run of Monte Carlo simulation to determine the threshold values of the design variable. The method is validated through illustrative examples and compares favorably with existing literature in terms of failure probabilities.
GEORISK-ASSESSMENT AND MANAGEMENT OF RISK FOR ENGINEERED SYSTEMS AND GEOHAZARDS
(2023)
Article
Engineering, Civil
Ke He, Robin Fell, Chongmin Song
Summary: This article investigates transverse cracking in embankment dams caused by cross-valley differential settlements, providing insights into the factors and possible forms of cracking, as well as general guidance on the width and depth of cracks. It emphasizes the need for site-specific numerical analyses to accurately simulate the actual conditions.
EUROPEAN JOURNAL OF ENVIRONMENTAL AND CIVIL ENGINEERING
(2022)
Article
Mechanics
Nikhil Garg, B. Gangadhara Prusty, Ean Tat Ooi, Chongmin Song, Garth Pearce, Andrew W. Phillips
COMPOSITE STRUCTURES
(2020)
Article
Engineering, Civil
A. Saputra, R. Behnke, W. Xing, C. Song, J. Schneider, M. Kaliske
Summary: Glass can be thermally prestressed and laminated with polymer foils to improve its load-bearing performance for civil engineering constructions. The post-fracture load-bearing performance of such polymer-glass assemblies is commonly assessed through large scale tests, but this research presents a numerical approach using digital image processing and finite element methods to evaluate the bending performance of fractured glass panels with polymer foils. The study aims to demonstrate the effectiveness of polymer foils in maintaining structural integrity after fracture.
ENGINEERING STRUCTURES
(2021)
Article
Engineering, Multidisciplinary
Shaima M. Dsouza, A. L. N. Pramod, Ean Tat Ooi, Chongmin Song, Sundararajan Natarajan
Summary: This paper proposes a robust framework based on the scaled boundary finite element method to model implicit interfaces in two-dimensional differential equations in nonhomogeneous media. The framework allows for interfaces to be implicitly defined, does not require special numerical integration techniques, and can work with efficient local mesh refinement. Numerical examples demonstrate the accuracy and convergence of the proposed technique compared to conforming finite element methods.
ENGINEERING ANALYSIS WITH BOUNDARY ELEMENTS
(2021)
Article
Mechanics
Hirshikesh, A. L. N. Pramod, Ean Tat Ooi, Chongmin Song, Sundararajan Natarajan
Summary: This work presents a framework for adaptive contact analysis in deformable solids, utilizing the SBFEM error indicator and quadtree decomposition, implemented and demonstrated using Abaqus for solving engineering significant contact problems.
EUROPEAN JOURNAL OF MECHANICS A-SOLIDS
(2021)
Article
Computer Science, Interdisciplinary Applications
Ke He, Chongmin Song, Robin Fell
Summary: This study presents the development of numerical simulation procedures for predicting the potential location, width and depth of transverse cracks in embankment dams, using a combination of conventional numerical and crack propagation modelling techniques.
COMPUTERS AND GEOTECHNICS
(2021)
Article
Engineering, Multidisciplinary
Chongmin Song, Sascha Eisentrager, Xiaoran Zhang
Summary: This paper introduces a high-order implicit time integration scheme for solving transient and wave propagation problems, which is computationally efficient and does not require direct inversion of the mass matrix. The derived second-order scheme is analytically equivalent to the Newmark constant average acceleration method, showcasing exceptional accuracy and efficiency in numerical examples compared to established second-order methods.
COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING
(2022)
Article
Computer Science, Interdisciplinary Applications
Yanling Qu, Denghong Chen, Lei Liu, Ean Tat Ooi, Sascha Eisentrager, Chongmin Song
Summary: This paper presents a direct time-domain procedure for seismic analysis of dam-reservoir-foundation interactions based on the scaled boundary finite element method (SBFEM). The method efficiently handles geometric complexity and seismic excitations using quadtree meshes and the Domain Reduction Method (DRM).
COMPUTERS AND GEOTECHNICS
(2021)
Article
Mechanics
M. D. Iqbal, C. Birk, E. T. Ooi, A. L. N. Pramod, S. Natarajan, H. Gravenkamp, C. Song
Summary: The scaled boundary finite element method is extended to model fracture in functionally graded materials under coupled thermo-mechanical loads. The proposed technique is validated through numerical examples for isotropic and orthotropic FGMs.
ENGINEERING FRACTURE MECHANICS
(2022)
Article
Engineering, Multidisciplinary
Ankit Ankit, Chongmin Song, Sascha Eisentrager, Sen Zhang, Ehab Hamed
Summary: This paper presents the development of a massively parallel explicit solver based on the central difference method (CDM) for the dynamic analysis of damage processes. The material degradation is incorporated using an integral-type non-local isotropic damage model, and a fully automatic preprocessing is enabled by following the octree-based mesh generation paradigm. The solver utilizes polyhedral elements and a pre-computation approach to handle neighbouring elements with different sizes, and employs mesh-partitioning technique and MPI directives for parallelization.
COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING
(2022)
Article
Engineering, Multidisciplinary
Junqi Zhang, Mi Zhao, Sascha Eisentraeger, Xiuli Du, Chongmin Song
Summary: This article introduces a parallel asynchronous explicit solver widely used in structural dynamics problems. It reduces computational costs by assigning different time step sizes to different parts of the mesh and improves performance and accuracy through the use of a balanced octree and a special polyhedral element formulation.
COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING
(2022)
Article
Engineering, Multidisciplinary
Ankit Ankit, Junqi Zhang, Sascha Eisentraeger, Chongmin Song
Summary: In this paper, a parallel preconditioned conjugate gradient (PCG) solver based on octree pattern is developed for large-scale elastostatic and implicit elastodynamic applications. The problem domain is discretized using octree cells for automatic mesh generation. Compatibility between neighboring octree cells is ensured by employing polyhedral elements. The solver performs matrix operations using an octree pattern-based pre-computation approach, reducing memory requirements and achieving efficient matrix product computations. Parallelism is achieved through mesh partitioning and MPI directives. The results show that the developed PCG solver achieves significant parallel speed-up and efficiency on distributed memory systems. The proposed framework is demonstrated through large-scale examples for CAD and image-based analyses.
COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING
(2023)
Article
Engineering, Geological
Shukai Ya, Sascha Eisentraeger, Yanling Qu, Junqi Zhang, Thomas Kuen, Chongmin Song
Summary: This paper presents an efficient numerical framework for seismic analysis of post-tensioned concrete gravity dams with automated insertion of anchors. The framework is implemented in ABAQUS using a polygonal user element derived by the scaled boundary finite element method (SBFEM). Post-tensioned anchors are naturally embedded into the structure by inserting nodes in the mesh and generating cohesive elements. The efficiency and accuracy of the proposed technique are demonstrated through numerical examples.
SOIL DYNAMICS AND EARTHQUAKE ENGINEERING
(2023)
Article
Engineering, Multidisciplinary
Dakshith Ruvin Wijesinghe, Sundararajan Natarajan, Greg You, Manoj Khandelwal, Ashley Dyson, Chongmin Song, Ean Tat Ooi
Summary: A scaled boundary finite element-based phase field formulation is proposed for modeling 2D fracture in saturated poroelastic media. An adaptive refinement strategy based on quadtree meshes is adopted to avoid the constraints of fine uniform meshes when using phase field models. The unique advantage of the scaled boundary finite element method allows for efficient computation on quadtree meshes without special treatment of hanging nodes. The proposed model is validated and demonstrated through numerical examples of hydraulic fractures.
COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING
(2023)
Article
Engineering, Multidisciplinary
B. Xiao, S. Natarajan, C. Birk, E. H. Ooi, C. Song, E. T. Ooi
Summary: This paper presents a general technique to develop arbitrary-sided polygonal elements based on the scaled boundary finite element method. The shape functions are derived from the solution of the Poisson's equation, which allows complete shape functions up to any specific order. These shape functions can be formulated on polygons with arbitrary number of sides and quadtree meshes. Well-established finite element procedures can be applied to solve various engineering problems using the developed shape functions.
INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING
(2023)
Article
Mathematics, Applied
Guo Zheng, Zengqiang Cao, Yuehaoxuan Wang, Reza Talemi
Summary: This study introduces two novel methods for predicting the fatigue response of Dynamic Cold Expansion (DCE) and Static Cold Expansion (SCE) open-hole plates. The accuracy of the prediction is enhanced by considering stress distributions and improving existing methods. The study also discusses the mechanisms behind fatigue life enhancement and fatigue crack propagation modes in cold expansion specimens.
FINITE ELEMENTS IN ANALYSIS AND DESIGN
(2024)
Article
Mathematics, Applied
Eric Heppner, Tomohiro Sasaki, Frank Trommer, Elmar Woschke
Summary: This paper presents a modeling approach for estimating the bonding strength of friction-welded lightweight structures. Through experiments and simulations, a method for evaluating the bonding strength of friction-welded lightweight structures is developed, and the plausibility and applicability of the model are discussed.
FINITE ELEMENTS IN ANALYSIS AND DESIGN
(2024)
Article
Mathematics, Applied
Piermario Vitullo, Alessio Colombo, Nicola Rares Franco, Andrea Manzoni, Paolo Zunino
Summary: Many applications in computational physics involve approximating problems with microstructure, characterized by multiple spatial scales in their data. However, these numerical solutions are often computationally expensive due to the need to capture fine details at small scales. Traditional projection based reduced order models (ROMs) fail to resolve these issues, even for second-order elliptic PDEs commonly found in engineering applications. To address this, we propose an alternative nonintrusive strategy to build a ROM, that combines classical proper orthogonal decomposition (POD) with a suitable neural network (NN) model to account for the small scales.
FINITE ELEMENTS IN ANALYSIS AND DESIGN
(2024)
Article
Mathematics, Applied
Chanh Dinh Vuong, Xiaofei Hu, Tinh Quoc Bui
Summary: In this paper, we present a dynamic description of the smoothing gradient-enhanced damage model for the simulation of quasi-brittle failure localization under time-dependent loading conditions. We introduce two efficient rate-dependent damage laws and various equivalent strain formulations to analyze the complicated stress states and inertia effects of the dynamic regime, enhancing the capability of the adopted approach in modeling dynamic fracture and branching.
FINITE ELEMENTS IN ANALYSIS AND DESIGN
(2024)
Article
Mathematics, Applied
Alexandre D. C. Amaro, A. Francisca Carvalho Alves, F. M. Andrade Pires
Summary: This study focuses on analyzing various deformation mechanisms that affect the behavior of PC/ABS blends using computational homogenization. By establishing a representative microstructural volume element, defining the constitutive description of the material phases, and modeling the interfaces and matrix damage, accurate predictions can be achieved. The findings have important implications for broader applications beyond PC/ABS blends.
FINITE ELEMENTS IN ANALYSIS AND DESIGN
(2024)
Article
Mathematics, Applied
David Hoffmeyer, A. R. Damanpack
Summary: This paper introduces a method for determining all six stress components for a cantilever-type beam that is subjected to concentrated end loads. The method considers an inhomogeneous cross-section and employs cylindrically orthotropic material properties. The efficacy of the method is validated by numerical examples and a benchmark example, and the analysis on a real sawn timber cross-section reveals significant disparities in the maximum stresses compared to conventional engineering approaches.
FINITE ELEMENTS IN ANALYSIS AND DESIGN
(2024)
Article
Mathematics, Applied
Vladimir Stojanovic, Jian Deng, Dunja Milic, Marko D. Petkovic
Summary: The present paper investigates the dynamic analysis of a coupled Timoshenko beam-beam or beam-arch mechanical system with geometric nonlinearities. A modified p-version finite element method is developed for the vibrations of a shear deformable coupled beam system with a discontinuity in an elastic layer. The main contribution of this work is the discovery of coupled effects and phenomena in the simultaneous vibration analysis of varying discontinuity and varying curvature of the newly modelled coupled mechanical system. The analysis results are valuable and have broader applications in the field of solids and structures.
FINITE ELEMENTS IN ANALYSIS AND DESIGN
(2024)
Article
Mathematics, Applied
Gihwan Kim, Phill-Seung Lee
Summary: The phantom-node method is applied in the phase field model for mesh coarsening to improve computational efficiency. By recovering the fine mesh in the crack path domain into a coarse mesh, this method significantly reduces the number of degrees of freedom involved in the computation.
FINITE ELEMENTS IN ANALYSIS AND DESIGN
(2024)
Article
Mathematics, Applied
Souhail Chaouch, Julien Yvonnet
Summary: In this study, an unsupervised machine learning-based clustering approach is developed to reduce the computational cost of nonlinear multiscale methods. The approach clusters macro Gauss points based on their mechanical states, reducing the problem from macro scale to micro scale. A single micro nonlinear Representative Volume Element (RVE) calculation is performed for each cluster, using a linear approximation of the macro stress. Anelastic macro strains are used to handle internal variables. The technique is applied to nonlinear hyperelastic, viscoelastic and elastoplastic composites.
FINITE ELEMENTS IN ANALYSIS AND DESIGN
(2024)
Article
Mathematics, Applied
Hoang-Giang Bui, Jelena Ninic, Christian Koch, Klaus Hackl, Guenther Meschke
Summary: With the increasing demand for underground transport infrastructures, it is crucial to develop methods and tools that efficiently explore design options and minimize risks to the environment. This study proposes a BIM-based approach that connects user-friendly software with effective simulation tools to analyze complex tunnel structures. The results show that modeling efforts and computational time can be significantly reduced while maintaining high accuracy.
FINITE ELEMENTS IN ANALYSIS AND DESIGN
(2024)
Article
Mathematics, Applied
Aslan Nasirov, Xiaoyu Zhang, David Wagner, Saikumar R. Yeratapally, Caglar Oskay
Summary: This manuscript presents an efficient model construction strategy for the eigenstrain homogenization method (EHM) for the reduced order models of the nonlinear response of heterogeneous microstructures. The strategy relies on a parallel, element-by-element, conjugate gradient solver, achieving near linear scaling with respect to the number of degrees of freedom used to resolve the microstructure. The linear scaling in the number of pre-analyses required to construct the reduced order model (ROM) follows from the EHM formulation. The developed framework has been verified using an additively manufactured polycrystalline microstructure of Inconel 625.
FINITE ELEMENTS IN ANALYSIS AND DESIGN
(2024)
Article
Mathematics, Applied
Atticus Beachy, Harok Bae, Jose A. Camberos, Ramana V. Grandhi
Summary: Emulator embedded neural networks leverage multi-fidelity data sources for efficient design exploration of aerospace engineering systems. However, training the ensemble models can be costly and pose computational challenges. This work presents a new type of emulator embedded neural network using the rapid neural network paradigm, which trains near-instantaneously without loss of prediction accuracy.
FINITE ELEMENTS IN ANALYSIS AND DESIGN
(2024)
Article
Mathematics, Applied
Arash Hajisharifi, Michele Girfoglio, Annalisa Quaini, Gianluigi Rozza
Summary: This paper introduces three reduced order models for reducing computational time in atmospheric flow simulation while preserving accuracy. Among them, the PODI method, which uses interpolation with radial basis functions, maintains accuracy at any time interval.
FINITE ELEMENTS IN ANALYSIS AND DESIGN
(2024)
Article
Mathematics, Applied
D. Munoz, S. Torregrosa, O. Allix, F. Chinesta
Summary: The Proper Generalized Decomposition (PGD) is a Model Order Reduction framework used for parametric analysis of physical problems. It allows for offline computation and real-time simulation in various situations. However, its efficiency may decrease when the domain itself is considered as a parameter. Optimal transport techniques have shown exceptional performance in interpolating fields over geometric domains with varying shapes. Therefore, combining these two techniques is a natural choice. PGD handles the parametric solution while the optimal transport-based methodology transports the solution for a family of domains defined by geometric parameters.
FINITE ELEMENTS IN ANALYSIS AND DESIGN
(2024)
Article
Mathematics, Applied
Jothi Mani Thondiraj, Akhshaya Paranikumar, Devesh Tiwari, Daniel Paquet, Pritam Chakraborty
Summary: This study develops a diffused interface CPFEM framework, which reduces computational cost by using biased mesh and provides accurate results using non-conformal elements in the mesh size transiting regions. The accuracy of the framework is confirmed through comparisons with sharp and stepped interface results.
FINITE ELEMENTS IN ANALYSIS AND DESIGN
(2024)
