Open AccessDOI
Review of the strain-based formulation for analysis of plane structures Part I: Formulation of basics and the existing elements
Mohammad Rezaiee-Pajand,Nima Gharaei-Moghaddam,Mohammadreza Ramezani +2 more
- Vol. 11, Iss: 2, pp 437-483
TLDR
A brief yet clear portrait of the basics and advantages of the direct strain-based method for development of high-performance plane finite elements and application and performance of the reviewed elements in the analysis of plane stress/strain problems is presented.Abstract:
Since the introduction of the finite element approach, as a numerical solution scheme for structural and solid mechanics applications, various for mulation methodologies have been proposed. These ways offer different advantages and shortcomings. Among these techniques, the standard displacement-based approach has attracted more interest due to its straightforward scheme and generality. Investigators have proved that the other strategies, such as the force-based, hybrid, assumed stress, and as sumed strain provides special advantages in comparison with the classicfinite elements. For instance, the mentioned techniques are able to solve difficulties, like shear locking, shear parasitic error, mesh sensitivity, poor convergence, and rotational dependency. The main goal of this two-part study is to present a brief yet clear portrait of the basics and advantages of the direct strain-based method for development of high-performance plane finite elements. In this article, which is the first part of this study, assump tions and the basics of this method are introduced. Then, a detailed review of all the existing strain-based membrane elements is presented. Although the strain formulation is applicable for different types of structures, most of the existing elements pertain to the plane structures. The second part of this study deals with the application and performance of the reviewed elements in the analysis of plane stress/strain problems.read more
Citations
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Book ChapterDOI
Introduction to the Finite Element Method
Nathan Ida,João P. A. Bastos +1 more
TL;DR: This chapter introduces the finite element method (FEM) as a tool for solution of classical electromagnetic problems and discusses the main points in the application to electromagnetic design, including formulation and implementation.
Journal ArticleDOI
Nonlinear dynamic analysis of FG/SMA/FG sandwich cylindrical shells using HSDT and semi ANS functions
TL;DR: In this article , a nonlinear dynamic analysis of FG/SMA/FG sandwich shells on elastic foundations subjected to the thermomechanical loading is performed for the first time.
Journal ArticleDOI
Linear and nonlinear mechanical responses of FG-GPLRC plates using a novel strain-based formulation of modified FSDT theory
TL;DR: In this paper , a composite finite element is proposed using the assumed natural strain (ANS) method, which is based on the unified strain interpolations and the minimized potential energy, and the linearized weak form of compatibility and equilibrium equations is obtained for the geometrically nonlinear analysis.
Journal ArticleDOI
Nonlinear thermomechanical analysis of CNTRC cylindrical shells using HSDT enriched by zig-zag and polyconvex strain cover functions
TL;DR: In this paper , a higher-order shear deformation zig-zag theory enriched by polyconvex strain cover functions is proposed for predicting the nonlinear stability characteristics of thermo mechanically loaded carbon nanotube-reinforced composite (CNTRC) laminated cylindrical shells surrounded by elastic foundations.
Review of the strain-based formulation for analysis of plane structures Part II: Evaluation of the numerical performance
TL;DR: In this article, several benchmark problems are solved to evaluate the performance of the existing strain-based membrane elements, which were reviewed in the first part, and the results indicated that the inclusion of drilling degrees of freedom and utilization of higher-order assumed strain field result in higher accuracy of the elements.
References
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Book ChapterDOI
Introduction to the Finite Element Method
Nathan Ida,João P. A. Bastos +1 more
TL;DR: This chapter introduces the finite element method (FEM) as a tool for solution of classical electromagnetic problems and discusses the main points in the application to electromagnetic design, including formulation and implementation.
Book
The Finite Element Method for Solid and Structural Mechanics
TL;DR: In this article, the Galerkin method of approximation is used to solve non-linear problems in solid mechanics and nonlinearity, such as finite deformation, contact and tied interfaces.
Journal ArticleDOI
Rational approach for assumed stress finite elements
Theodore H. H. Pian,K. Sumihara +1 more
TL;DR: In this paper, a new method for the formulation of hybrid elements by the Hellinger-Reissner principle is established by expanding the essential terms of the assumed stresses as complete polynomials in the natural coordinates of the element.
Journal ArticleDOI
A non-conforming element for stress analysis
Journal ArticleDOI
A simple and efficient finite element for plate bending
TL;DR: In this paper, a simple and efficient finite element is introduced for plate bending applications, where Bilinear displacement and rotation functions are employed in conjunction with selective reduced integration, and the element is surprisingly accurate.