Article
Computer Science, Interdisciplinary Applications
Mengkai Lu, Liang Zhang, Zhou Yan, Jian Wu
Summary: The paper presents a variational principle for bi-modulus elasticity to model no-tension/compression materials and structures, proving equivalence between the derived complementarity finite element formulation and a variational inequality. The method is demonstrated through numerical examples and verified with existing experimental data, showing good numerical stability and improved computational efficiency.
COMPUTERS & STRUCTURES
(2021)
Article
Mathematics, Applied
Erhan Bayraktar, Ibrahim Ekren, Xin Zhang
Summary: In this note, a smooth variational principle on Wasserstein space is provided by constructing a smooth gauge-type function using the sliced Wasserstein distance. This function is a crucial tool for optimization problems and viscosity theory of PDEs on Wasserstein space.
PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY
(2023)
Article
Mathematics
Xiao-Ting He, Xiao-Guang Wang, Bo Pang, Jie-Chuan Ai, Jun-Yi Sun
Summary: In this study, the variational method and numerical simulation technique were used to solve the problem of bimodular functionally graded thin plates under large deformation. The variational method was applied to establish a functional based on the elastic strain energy of the plate and the undetermined coefficients in the functional were changed to achieve variation. The numerical simulation technique was utilized to simulate the bimodular effect and functionally graded properties of the materials. The results showed agreement between the numerical simulation and variational solution, validating the effectiveness of the variational solution obtained.
Article
Computer Science, Interdisciplinary Applications
Dhiraj S. Bombarde, Manish Agrawal, Sachin S. Gautam, Arup Nandy
Summary: The study introduces a novel twenty-seven node quadratic EAS element, addressing the underutilization of quadratic elements in existing 3D EAS elements. Additionally, a six-node wedge and an eighteen-node wedge EAS element are presented in the manuscript.
COMPUTERS & STRUCTURES
(2024)
Article
Mathematics, Applied
S. Ali Faghidian, Krzysztof Kamil Zur, Isaac Elishakoff
Summary: This study utilizes the mixture unified gradient theory of elasticity to investigate the nanoscopic nonlinear flexure mechanics of nanobeams. Through a mixed variational framework and numerical approach, the size-effect phenomenon associated with stress gradient, strain gradient, and classical elasticity theories is realized and the nonlinear flexural characteristics of nano-sized beams are detected and compared.
COMMUNICATIONS IN NONLINEAR SCIENCE AND NUMERICAL SIMULATION
(2023)
Article
Engineering, Multidisciplinary
Huilong Ren, Xiaoying Zhuang, Nguyen-Thoi Trung, Timon Rabczuk
Summary: A general finite deformation higher-order gradient elasticity theory is proposed in the paper, reducing the material parameters significantly under certain simplifications. A nonlocal operator method is developed and applied to numerical examples, demonstrating the stiffness response of the high gradient solid theory and the capability of the nonlocal operator method in solving higher-order physical problems.
COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING
(2021)
Article
Thermodynamics
Vincenzo Tibullo, Martina Nunziata
Summary: This article discusses the results of the linear theory of thermopiezoelectricity. It provides a brief introduction to dielectric materials and the phenomena of direct and inverse piezoelectricity. The article then presents a general theory of thermopiezoelectricity for strain gradient materials, where the second gradient of the displacement field and electric potential are considered as independent constitutive variables. The second law of thermodynamics is formulated based on the entropy production inequality proposed by Green and Laws, and thermodynamic restrictions are obtained. The article also establishes linear constitutive equations and the mixed initial-boundary value problem. Based on this theory, uniqueness result and a variational principle are obtained.
JOURNAL OF THERMAL STRESSES
(2023)
Article
Mathematics, Applied
Wenfang Yao, Xiaoqi Yang
Summary: This paper investigates upper estimates of the projectional coderivative of implicit mappings and their applications in analyzing the relative Lipschitz-like property. The paper provides upper estimates of the projectional coderivative for solution mappings of parametric systems under different constraint qualifications. For the solution mapping of affine variational inequalities, a generalized critical face condition is obtained to determine the sufficiency of its Lipschitz-like property relative to a polyhedral set within its domain under a constraint qualification. The necessity can also be obtained under certain regularity conditions or when the polyhedral set further becomes the domain of the solution mapping. Possible conditions for the necessity are further discussed, and a solution mapping of a linear complementarity problem with a Q0 matrix is considered as an example.
SIAM JOURNAL ON OPTIMIZATION
(2023)
Article
Chemistry, Physical
Xiao-Ting He, Xin Wang, Meng-Qiao Zhang, Jun-Yi Sun
Summary: This study investigates the thermal stress problem of bimodular curved beams subjected to end-side concentrated shear force, considering arbitrary temperature rise modes. Through theoretical analysis and numerical simulation, a two-dimensional thermoelastic solution of the bimodular curved beam is obtained. The results show that the solution for a bimodular curved beam with a thermal effect can be simplified to that without a thermal effect. The numerical simulation validates the accuracy of the theoretical solution. These findings provide a theoretical reference for the refined analysis and optimization of curved beams in a thermal environment.
Article
Mechanics
Laura Galuppi, Gianni Royer-Carfagni
Summary: This article presents a solution for the strain issue caused by temperature variations in the structural design of glazed surfaces. The proposed semi-analytical approach, implemented in a finite element code, evaluates the time-dependent temperature profile through the thickness of layered glazing. It rigorously considers energy conservation and is particularly effective for problems with steep temperature variations.
INTERNATIONAL JOURNAL OF SOLIDS AND STRUCTURES
(2022)
Article
Engineering, Mechanical
Seyed Ali Faghidian, Abdelouahed Tounsi
Summary: The dynamic characteristics of elastic nanobeams are rigorously analyzed using the mixture unified gradient theory of elasticity, with closed-form solutions and numerical evaluations. The study shows that the established elasticity model effectively describes the softening and stiffening responses of nanobeams, providing a practical approach to tackle dynamics of nano-structures.
FACTA UNIVERSITATIS-SERIES MECHANICAL ENGINEERING
(2022)
Article
Engineering, Mechanical
J. Zhang, J. F. Shao, Q. Z. Zhu, G. De Saxce
Summary: A new homogenization model is developed for porous media, with a macroscopic fatigue criterion being established based on the variational principle. Dirac's measure is adopted to simplify the volume integral, showing the dependence of the plastic shakedown limit load on the invariants of the macroscopic stress tensor. The new criterion significantly improves the accuracy of plastic shakedown limit prediction for porous materials with large values of porosity.
INTERNATIONAL JOURNAL OF MECHANICAL SCIENCES
(2021)
Article
Materials Science, Multidisciplinary
Sandipan Paul, Alan D. Freed
Summary: In this study, a constitutive model for elastic-plastic materials is developed using scalar, conjugate, stress-strain, base pairs in a finite deformation setting. The alternative QR decomposition of the deformation gradient allows for direct measurement of Laplace stretch and its plastic contributions. This model has implications for the construction of constitutive models for a wider class of materials.
JOURNAL OF THE MECHANICS AND PHYSICS OF SOLIDS
(2021)
Article
Mathematics, Applied
Chaemin Lee, Jongho Park
Summary: This study establishes a rigorous mathematical foundation for the convergence properties of the strain-smoothed element (SSE) method. The unique feature of the SSE method is the construction of smoothed strain fields by unifying the strains of adjacent elements, requiring convergence analysis different from other existing methods. By proposing a novel mixed variational principle and analyzing the SSE method in comparison to other existing methods, the study explains the improved convergence behavior and presents numerical experiments to support the theoretical results.
COMPUTERS & MATHEMATICS WITH APPLICATIONS
(2021)
Article
Mathematics, Interdisciplinary Applications
Shuai-Jia Kou, Chun-Hui He, Xing-Chen Men, Ji-Huan He
Summary: This paper introduces the application of fractal calculus in studying the non-smooth boundary layer of a viscous fluid, and proposes a fractal-fractional modification of the Blasius equation, which is solved analytically. The results show that a non-smooth boundary may lead to smaller friction, which can explain phenomena such as the lotus effect, waving sand dunes, and water collection on Fangzhu's leaf. The fractal boundary layer theory opens up a new approach to optimizing the design of highly moving surfaces with minimal friction.
FRACTALS-COMPLEX GEOMETRY PATTERNS AND SCALING IN NATURE AND SOCIETY
(2022)
