Article
Engineering, Civil
Hanxing Zhao, Xin Lan, Liwu Liu, Yanju Liu, Jinsong Leng
Summary: The buckling loads and geometric imperfections sensitivities of SMPC cylindrical shells at different temperatures were determined through numerical simulations and experimental analyses. The results show that the buckling loads obtained by numerical techniques are sensitive to temperature, while the knock-down factors (KDFs) are not. Brittle fracture is the main failure mode at low temperature, posing a risk for design using numerical techniques in this region. At high temperatures, the single perturbation displacement imperfection (SPDI) method overestimates the KDFs, while the KDFs calculated by the multiple perturbation displacement imperfection (MPDI) and linear buckling mode imperfection (LBMI) techniques are in good agreement with experimental results. The LBMI method is able to distinguish the influence of temperature on post-buckling patterns and has better consistency with experiments.
THIN-WALLED STRUCTURES
(2023)
Review
Engineering, Mechanical
Bo Wang, Peng Hao, Xiangtao Ma, Kuo Tian
Summary: Thin-walled structures are commonly used in aerospace and aircraft structures, but accurately predicting the lower-bound buckling load is still a challenge due to geometric imperfections. This paper reviews several new numerical and experimental methods for determining knockdown factors (KDF) and proposes an improved KDF curve based on extensive test data. The new KDFs show an overall improvement compared to the traditional criterion.
ACTA MECHANICA SINICA
(2022)
Article
Engineering, Civil
V. Krasovsky, A. Evkin
Summary: The experimental studies on buckling of dented axially compressed unstiffened cylindrical shells show that the buckling behavior can be described by plateaus, and the lower local buckling loads are slightly influenced by geometric imperfections.
THIN-WALLED STRUCTURES
(2021)
Article
Engineering, Civil
Ruihai Xin, Vinh Tung Le, Nam Seo Goo
Summary: In this study, the global-local buckling phenomenon in shell structures was investigated using a multi-Digital Image Correlation (DIC) technique. Experimental and numerical analysis were conducted to confirm the findings.
THIN-WALLED STRUCTURES
(2022)
Article
Engineering, Civil
Guangxin Sun, Shengbo Zhu, Rumin Teng, Jiabin Sun, Zhenhuan Zhou, Xinsheng Xu
Summary: In this study, the post-buckling behavior of composite porous cylindrical shells under axial compression and hydrostatic pressure is investigated using the moderately thick shell theory. The accuracy of the solutions is validated by comparing them with existing theoretical and experimental data. The study reveals that the geometry and material properties significantly affect the post-buckling behavior and knockdown factor of the cylindrical shell, and also explains and discusses the discrepancies between the classical thin-walled shell theory and the moderately thick shell theory.
THIN-WALLED STRUCTURES
(2022)
Article
Mechanics
Zbigniew Kolakowski, Andrzej Teter
Summary: The behavior of FGM cylindrical shells with imperfections under compression was analyzed using an analytical-numerical method. The critical load and imperfection sensitivity surface of real structures were determined. The material gradient and support conditions of the shell were taken into account in the calculations. This research provides insights for the design and verification of shell structures.
COMPOSITE STRUCTURES
(2022)
Article
Multidisciplinary Sciences
R. M. J. Groh, A. Pirrera
Summary: This article proposes a method of establishing shell buckling knockdown factors using localized probing, which can trigger both single-dimple and double-dimple edge states. Three design curves of varying conservatism are derived based on the stability features of probing, providing a more flexible approach to structural design than legacy knockdown factors. The most conservative design curve bounds a large dataset of experimental buckling results from below, highlighting its significance in efficient structural design.
PHILOSOPHICAL TRANSACTIONS OF THE ROYAL SOCIETY A-MATHEMATICAL PHYSICAL AND ENGINEERING SCIENCES
(2023)
Article
Mathematics, Applied
Davit Harutyunyan, Andre Martins Rodrigues
Summary: This study proves that the buckling load of cylindrical shells under vertical compression depends on the curvature of the cross section curve. For convex curves with uniformly positive curvature, the buckling load has a linear relationship with the shell thickness. For curves with positive curvature at finitely many points, the buckling load lies between C(1)h(8/5) and C(2)h(3/2) for small thickness h > 0.
JOURNAL OF NONLINEAR SCIENCE
(2023)
Article
Multidisciplinary Sciences
Abubakr E. S. Musa, Madyan A. Al-Shugaa, Husain J. Al-Gahtani
Summary: Buckling is the most common type of failure for circular cylindrical shells subjected to axial compressive forces. The buckling stress of these shells is highly affected by geometric imperfections, such as localized damage (dents), which significantly reduce the buckling strength. This study numerically investigates the effect of dent imperfections on the buckling strength of shells with large R/t ratios, finding that dent size, depth, and position do not show a remarkable trend in their relationship with the reduction in buckling strength.
ARABIAN JOURNAL FOR SCIENCE AND ENGINEERING
(2023)
Article
Engineering, Multidisciplinary
Haoran Wang, Johann Guilleminot, Benjamin W. Schafer, Mazdak Tootkaboni
Summary: Buckling of thin-shell structures is a classic problem in mechanics. In this study, we investigate the buckling behavior of imperfect cylindrical shells using a novel representation of the stochastically imperfect shell geometry. Through finite element analysis, we gain new insights into the interplay between random imperfections and topological features that influence buckling behavior.
COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING
(2022)
Article
Materials Science, Multidisciplinary
Arefeh Abbasi, Dong Yan, Pedro M. Reis
Summary: This study focuses on the mechanical response of pressurized spherical shells with a single dimple-like defect to a point probe, characterizing the nonlinear force-indentation response at different pressurization levels through experiments, finite element modeling, and classic shell theory. The critical buckling pressure of the shell can be inferred non-destructively by tracking the maxima of the indentation force-displacement curves, with the effectiveness of probing influenced by the indentation angle. The study also quantifies the characteristic length associated with localized deformation using FEM simulations and shallow shell theory, demonstrating the limitations of applying probing as a non-destructive technique to assess the stability of spherical shells.
JOURNAL OF THE MECHANICS AND PHYSICS OF SOLIDS
(2021)
Article
Engineering, Civil
Abubakr E. S. Musa, Madyan A. Al-Shugaa, Husain J. Al-Gahtani
Summary: This study investigates the buckling behavior of metal cylindrical shells subjected to axial compressions. The research highlights the complex interaction between intended and unintended geometric imperfections in experimental investigations, making it challenging to identify the sole effect of either one. A simple approximate procedure is proposed to account for the effect of unintended imperfections in order to evaluate the buckling strength reduction due to certain intended forms of imperfection. The study also suggests general recommendations for conducting combined experimental-numerical parametric studies.
THIN-WALLED STRUCTURES
(2021)
Article
Acoustics
Felipe Franzoni, Adrian Gliszczynski, Theodor Dan Baciu, Mariano Andres Arbelo, Richard Degenhardt
Summary: This study investigates the application of the vibration correlation technique to determine the in-situ buckling load of unstiffened and skin-dominated stiffened cylindrical shells. The study proposes the use of a load factor to enhance the buckling load estimations based on validated finite element models and numerical results. Experimental results are also reevaluated to assess the impact of the load factor on the buckling load predictions.
JOURNAL OF SOUND AND VIBRATION
(2022)
Article
Engineering, Civil
Lei Chen, Kapnang Franky, Hao Zhang, Xiaoli Xiong
Summary: Most research focuses on high-strength steel axial compression members, but few studies investigate the mechanical behavior of high-strength steel cylindrical shells in bending. This paper explores their load-bearing capacity under global bending, considering factors such as residual stress and material plasticity. The results provide valuable information for the design of high-strength steel cylindrical shells.
Article
Materials Science, Multidisciplinary
Tianzhen Liu, Yuzhen Chen, John W. Hutchinson, Lihua Jin
Summary: Viscoelastic spherical shells exhibit a wide range of time/rate-dependent buckling behaviors, including creep buckling, which occurs after a time delay. This study develops an analytical model to understand the nonlinear time-dependent buckling behavior of these shells, considering geometric imperfections and two types of loading: prescribed rate of volume change and constant pressure. The results demonstrate the important roles of viscoelasticity and loading rates in the load-carrying behavior, and reveal a connection between short-time elastic buckling and long-time creep buckling limits.
JOURNAL OF THE MECHANICS AND PHYSICS OF SOLIDS
(2022)
Article
Computer Science, Interdisciplinary Applications
Reza Kolahchi, Kuo Tian, Behrooz Keshtegar, Zengcong Li, Nguyen-Thoi Trung, Duc-Kien Thai
Summary: A novel hybrid optimization method is proposed in this study, combining active Kriging and grey wolf optimizer to improve the accuracy of predicted optimum results for load-carrying capacity of hierarchical stiffened shells. The method enhances the accuracy of optimum load-carrying capacity by about 10% compared to other models, and increases the load-carrying by about 2% compared to the Kriging model.
ENGINEERING WITH COMPUTERS
(2022)
Article
Computer Science, Interdisciplinary Applications
Zengcong Li, Tianhe Gao, Kuo Tian, Bo Wang
Summary: A novel elite-driven surrogate-assisted Covariance Matrix Adaptation Evolution Strategy (ES-CMA-ES) algorithm based on the improved Lower Confidence Bound (ILCB) method is proposed in this paper to relieve computational burden and improve global optimizing ability. By introducing step size to control the uncertainty term of the ILCB formula adaptively, along with an efficient pre-screening strategy and a competitive chaotic operator for model management, ES-CMA-ES achieves efficient candidate point sampling, optimization convergence acceleration, and avoidance of local optima trapping. The proposed algorithm shows outstanding efficiency, global optimizing ability, and applicability compared to other black-box optimization algorithms.
ENGINEERING WITH COMPUTERS
(2023)
Article
Mechanics
Kuo Tian, Lei Huang, Yu Sun, Liang Zhao, Tianhe Gao, Bo Wang
Summary: This paper introduces the application of numerical VCT (NVCT) in predicting buckling load, presents the NVCT formula for cylindrical shell buckling load, and combines it with the combined approximation (CA) method. The high efficiency and accuracy of CA-NVCT in buckling analysis and optimization are verified through comparison with experimental results and typical numerical methods.
EUROPEAN JOURNAL OF MECHANICS A-SOLIDS
(2022)
Article
Materials Science, Multidisciplinary
Lei Huang, Hongqing Li, Kaiwei Zheng, Kuo Tian, Bo Wang
Summary: This article proposes a shape optimization method for axisymmetric disks based on radial basis function (RBF) mesh deformation and Laplace smoothing approaches. The method uses a greedy algorithm to obtain an optimized reduced control point selection of mesh deformation under the influence of the design space. RBF mesh deformation is used to change the axisymmetric contour shape, and Laplace smoothing is employed to monitor and improve the local mesh quality. The proposed method is validated through two examples in aero-engines, demonstrating its significant potential in reducing the maximum equivalent stress of axisymmetric disks.
MECHANICS OF ADVANCED MATERIALS AND STRUCTURES
(2023)
Article
Computer Science, Artificial Intelligence
Zengcong Li, Shu Zhang, Hongqing Li, Kuo Tian, Zhizhong Cheng, Yan Chen, Bo Wang
Summary: In this paper, a novel method called on-line transfer learning based multi-fidelity data fusion (OTL-MFDF) is proposed to improve the prediction accuracy of DNN. The method includes two parts: establishing an ensemble model of DNNs and developing an on-line learning system for adaptive updating. Experimental results demonstrate the effectiveness, global prediction accuracy, and applicability of the OTL-MFDF method.
ADVANCED ENGINEERING INFORMATICS
(2022)
Article
Materials Science, Multidisciplinary
Lei Huang, Qiushi Xia, Tianhe Gao, Bo Wang, Kuo Tian
Summary: This paper proposes a numerical prediction method for buckling loads in shell structures under axial compression and thermal loads based on vibration correlation technique (VCT). The method, named numerical VCT (NVCT), is a non-destructive test method that can be realized numerically. The paper presents the derivation of the VCT formula for thin-walled structures and introduces an adaptive step-size NVCT (AS-NVCT) calculation scheme based on an adaptive increment control strategy. The findings demonstrate that AS-NVCT achieves accurate buckling prediction results and higher efficiency compared to typical numerical buckling methods.
MULTIDISCIPLINE MODELING IN MATERIALS AND STRUCTURES
(2022)
Article
Computer Science, Interdisciplinary Applications
Yu Sun, Zitong Zhou, Pingtao Lai, Hongqing Li, Guangming Wang, Bo Wang, Kuo Tian
Summary: This study presents an optimization framework based on isogeometric analysis, which can simultaneously optimize the size and layout of stiffeners to maximize the buckling load of the grid-stiffened shell. Typical examples are used to validate the effectiveness and efficiency of the framework, and the impact of initial stiffener layouts and heights on the optimization results are discussed in detail. The optimization results show that the proposed framework can achieve novel grid-stiffened shells with significantly improved load-carrying capacity compared to traditional orthogonal grid-stiffened shells.
STRUCTURAL AND MULTIDISCIPLINARY OPTIMIZATION
(2022)
Article
Chemistry, Multidisciplinary
Yongxin Shi, Zhao Ke, Wei Sun, Peng Zhang, Qiang Yang, Kuo Tian
Summary: This study proposes a fast vibration reduction optimization approach accelerated by the global proper orthogonal decomposition (POD) reduced-order model (ROM) to increase the efficiency of frequency response analysis and vibration reduction optimization of complex thin-walled shells. The global POD ROM is adaptively updated using the CV-Voronoi sequence sampling method to achieve higher global prediction accuracy. The fast vibration reduction optimization is performed by combining the surrogate-based efficient global optimization (EGO) method and the proposed ROM, achieving high prediction accuracy and efficiency.
APPLIED SCIENCES-BASEL
(2023)
Article
Computer Science, Interdisciplinary Applications
Lei Huang, Tianhe Gao, Zhiyong Sun, Bo Wang, Kuo Tian
Summary: Topology and shape optimization is a powerful technique for achieving high-stiffness configurations of curved shells. This paper presents a developed shape-dependent topology optimization method and an integrated topology and shape optimization framework. The framework combines shape optimization design variables and topology optimization stiffener constraints through mesh deformation approach, and utilizes a deep neural network surrogate model for acceleration. The proposed framework is demonstrated to be effective in three engineering examples.
ENGINEERING WITH COMPUTERS
(2023)
Review
Chemistry, Multidisciplinary
Zhiyong Zhou, Chenfan Yu, Xiuzhu Han, Kaiwei Zheng, Chao Jiang, Kuo Tian
Summary: The pressurized capsule structure is crucial for manned spacecraft as it provides the necessary pressure environment for astronauts or payloads in space. However, the conventional welded panel pressurized capsule structure faces challenges in meeting the requirements of manned deep space exploration missions. This paper comprehensively explains the limitations of the current structure and proposes a new integrated panel pressurized capsule structure that offers lightweight advantages. The technical details and research results of the new structure are also presented, providing valuable references for the future development of large-size, lightweight pressurized capsule structures.
APPLIED SCIENCES-BASEL
(2023)
Article
Materials Science, Composites
Yunfei Deng, Yao Deng, Wenquan Liu, Shitong Zhang, Kuo Tian
Summary: Glass fiber trapezoidal corrugated sandwich structures consisting of trapezoidal cores and glass fiber-reinforced polymer (GFRP) panels were investigated through a series of low-velocity impact tests. The study considered the effects of impact position, impactor shape, and impactor diameter on the damage mechanism of the sandwich structures. The results showed that the maximum impact load occurred at the node impact point, while the displacement of impact was significantly higher at the base. It was also observed that a smaller contact surface of the impactor resulted in more concentrated stress and lower required penetration energy.
JOURNAL OF COMPOSITES SCIENCE
(2023)
Article
Materials Science, Composites
Wei Sun, Junyi Xiao, Xuanwei Hu, Baoxin Hao, Huan Zhang, Peng Zhang, Tianhe Gao, Kuo Tian
Summary: By conducting tests on 10 specimens with different parameters, it was found that the strength of the honeycomb sandwich structure is directly proportional to the thickness of the skin, the density of the honeycomb core cells, and the size of the embedded parts. Considering the accuracy retention ability of the structure under load, the allowable load of the embedded parts is about 90% of the yield load.
JOURNAL OF COMPOSITES SCIENCE
(2023)
Article
Engineering, Aerospace
Ziyu Xu, Tianhe Gao, Zengcong Li, Qingjie Bi, Xiongwei Liu, Kuo Tian
Summary: This paper proposes a digital twin modeling method of multi-source data fusion based on transfer learning for the strength evaluation of spacecraft stiffened plate structures. By utilizing simulation data and sensor data as the source and target dataset respectively, a digital twin model is built to visualize the full-field strength information. Experimental results verify the effectiveness and potential of the proposed method.
Article
Engineering, Aerospace
Tianhe Gao, Ziyu Xu, Zengcong Li, Pei Liu, Kuo Tian
Summary: A two-stage intelligent method for the layout design of the curved cabin door is proposed, which combines topology optimization and evolutionary algorithm to achieve an innovative and optimal design. The experimental results demonstrate the effectiveness of the proposed method in reducing mass while satisfying constraints, indicating its potential in improving the carrying capacity and efficiency of spacecraft.
Review
Engineering, Mechanical
Bo Wang, Peng Hao, Xiangtao Ma, Kuo Tian
Summary: Thin-walled structures are commonly used in aerospace and aircraft structures, but accurately predicting the lower-bound buckling load is still a challenge due to geometric imperfections. This paper reviews several new numerical and experimental methods for determining knockdown factors (KDF) and proposes an improved KDF curve based on extensive test data. The new KDFs show an overall improvement compared to the traditional criterion.
ACTA MECHANICA SINICA
(2022)
Article
Mechanics
Zhiqiang Meng, Xu Gao, Hujie Yan, Mingchao Liu, Huijie Cao, Tie Mei, Chang Qing Chen
Summary: This paper presents a cage-shaped, self-folding mechanical metamaterial that exhibits multiple deformation modes and has tunable mechanical properties, providing multifunctional applications in various fields.
INTERNATIONAL JOURNAL OF SOLIDS AND STRUCTURES
(2024)
Article
Mechanics
Hasan Murat Oztemiz, Semsettin Temiz
Summary: Sandwich panel composites have various applications and their mechanical behavior and performance depend on material properties and geometry. The load-carrying capacity of S-core composite sandwich panels increases with the increase of the core wall thickness, but decreases with the increase of the core height.
INTERNATIONAL JOURNAL OF SOLIDS AND STRUCTURES
(2024)
Article
Mechanics
Yang Sun, Wei Zhang, Weipeng Hu, Mabao Liu
Summary: The study presents a novel computational framework to investigate the effect of graphene percolation network on the strength-ductility of graphene/metal composites. It utilizes the Cauchy's probabilistic model, the field fluctuation method, and the irreversible thermodynamics principle.
INTERNATIONAL JOURNAL OF SOLIDS AND STRUCTURES
(2024)
Article
Mechanics
Elaheh Kazemi-Khasragh, Juan P. Fernandez Blazquez, David Garoz Gomez, Carlos Gonzalez, Maciej Haranczyk
Summary: This study explores group interaction modelling (GIM) and machine learning (ML) approaches for predicting thermal and mechanical properties of polymers. ML approach offers more reliable predictions compared to GIM, which is highly dependent on the accuracy of input parameters.
INTERNATIONAL JOURNAL OF SOLIDS AND STRUCTURES
(2024)
Article
Mechanics
Yafei Yin, Shaotong Dong, Dong Wu, Min Li, Yuhang Li
Summary: This paper investigates a bending-induced instability in sandwiched composite structures, and establishes a phase diagram to predict its characteristics. The results are of great significance in understanding the physical mechanisms of bending instability and providing design guidelines for practical applications.
INTERNATIONAL JOURNAL OF SOLIDS AND STRUCTURES
(2024)
Article
Mechanics
Dhairya R. Vyas, Sharen J. Cummins, Gary W. Delaney, Murray Rudman, Devang V. Khakhar
Summary: In this study, multiple collisions of granules on a substrate are analyzed using Collisional Smooth Particle Hydrodynamics (CSPH) to understand the influence of impact-induced deformation on subsequent collision dynamics. It is found that the collision dynamics are dependent on the impact location and the deformation caused by preceding impacts. The accuracy of three theoretical models is also evaluated by comparing their predictions with CSPH results, and it is discovered that these models are only useful for predicting collisions at the same location repeatedly.
INTERNATIONAL JOURNAL OF SOLIDS AND STRUCTURES
(2024)
Article
Mechanics
Sneha B. Cheryala, Chandra S. Yerramalli
Summary: The effect of hybridization on the growth of interface crack along the fiber is predicted. The study shows an enhancement in the compressive splitting strength with hybridization due to the lateral confinement effect on the interfacial crack.
INTERNATIONAL JOURNAL OF SOLIDS AND STRUCTURES
(2024)
Article
Mechanics
Xiang-Nan Li, Xiao-Bao Zuo, Liang Li, Jing-Han Liu
Summary: A multiscale mechanical model is proposed to quantitatively describe the macro-mechanical behavior of fiber reinforced concrete (FRC) based on its multiscale material compositions. The model establishes the stiffness and strength equations for each scale of FRC and demonstrates the influence of steel fiber parameters on the mechanical properties of FRC.
INTERNATIONAL JOURNAL OF SOLIDS AND STRUCTURES
(2024)
Article
Mechanics
Vicente Ramirez-Luis, Hilario Hernandez-Moreno, Orlando Susarrey-Huerta
Summary: In this paper, a Multicell Thin-walled Method is developed for studying the stress distributions in multimaterial beams. This method accurately obtains complex stress fields while reducing the solution time and computational cost. Validation with the finite element method confirms the accuracy of the proposed method.
INTERNATIONAL JOURNAL OF SOLIDS AND STRUCTURES
(2024)
Article
Mechanics
Yanfeng Zheng, Siyuan Li, Jingyao Zhang, Yaozhi Luo
Summary: This study proposes an enhanced simplified model based on finite particle method (FPM) to consider the link cross-sectional size and contact in Bennett linkages. The model introduces virtual beams and contact forces to accurately simulate the real-world behavior of Bennett linkages. The proposed method is effective for dynamic analysis of large-scale deployable Bennett linkages and shows great potential.
INTERNATIONAL JOURNAL OF SOLIDS AND STRUCTURES
(2024)
Article
Mechanics
Viktoriya Pasternak, Heorhiy Sulym, Iaroslav M. Pasternak
Summary: This paper investigates anisotropic elastic, magnetoelectroelastic, and quasicrystal solids and presents their equations of time-harmonic motion and constitutive relations in a compact and unified form. A matrix approach is proposed to derive the 3D time-harmonic Green's functions for these materials. The effects of phason field dynamics on the phonon oscillations in quasicrystals are studied in detail. The paper provides a strict proof that the eigenvalues of the time-harmonic magnetoelectroelaticity problem are all positive. It also demonstrates the application of the obtained time-harmonic Green's functions in solving boundary value problems for these materials using the derived boundary integral equations.
INTERNATIONAL JOURNAL OF SOLIDS AND STRUCTURES
(2024)
Article
Mechanics
Jan Tomec, Gordan Jelenic
Summary: This paper investigates the relationship between different formulations and contact-force models in beam-to-beam contact mechanics. It specifically addresses the recently developed mortar method and develops its variant based on the penalty method. The developed elements are tested using the same examples to provide an objective comparison in terms of robustness and computational cost.
INTERNATIONAL JOURNAL OF SOLIDS AND STRUCTURES
(2024)
Article
Mechanics
Paulo Teixeira Goncalves, Albertino Arteiro, Nuno Rocha, Fermin Otero
Summary: This work presents a novel formulation of a 3D smeared crack model for unidirectional fiber-reinforced polymer composites based on a stress invariant approach for transverse yielding and failure initiation. The performance of the model is evaluated using monotonic and non-monotonic damage evolution, verified with single element tests and compared with experimental results.
INTERNATIONAL JOURNAL OF SOLIDS AND STRUCTURES
(2024)
Article
Mechanics
Hanbin Yin, Yinji Ma, Xue Feng
Summary: This paper investigates the peeling behavior of a viscoelastic film bonded to a rigid substrate and establishes a theoretical peeling model. The study reveals three typical relationships between the peeling force and peeling velocity, which depend on the viscous dissipation within the film and the rate-dependent adhesion at the interface. Additionally, factors such as film thickness, interfacial toughness, and interfacial strength are identified as influencing the steady-state peeling force.
INTERNATIONAL JOURNAL OF SOLIDS AND STRUCTURES
(2024)
Article
Mechanics
Peter Noe Poulsen, John Forbes Olesen
Summary: Finite Element Limit Analysis (FELA) is increasingly used to calculate the ultimate bearing capacity of structures made of ductile materials. This study presents a consistent and general weak formulation based on virtual work for both the lower and upper bound problem, ensuring uniqueness of the optimal solution. A plane element with linear stress variation and quadratic displacement field is introduced, showing good results for load level, stress distribution, and collapse mechanism even for coarse meshes in verification and reinforced concrete examples.
INTERNATIONAL JOURNAL OF SOLIDS AND STRUCTURES
(2024)