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The Finite Element Method for Solid and Structural Mechanics
07 Nov 2013-
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.
Abstract: General Problems in solid mechanics and non-linearity Galerkin method of approximation - irreducible and mixed forms Solution of non-linear algebraic equations Inelastic and non-linear materials Geometrically non-linear problems - finite deformation Material constitution for finite deformation Treatment of Constraints - contact and tied interfaces Pseudo-Rigid & Rigid-Flexible Bodies Discrete element methods Structural Mechanics Problems in One Dimension - rods Plate Bending Approximation Thick Reissner-Mindlin Plates -Irreducible & Mixed Formulations Shells as an assembly of flat elements Curved rods and axisymmetric shells Shells as a special case of three-dimensional analysis Semi-analytical finite element processes Non-linear structural processes - large displacement and instability Multiscale modelling Computer procedures for finite element analysis Appendices
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TL;DR: In this paper, a review of continuum-based variational formulations for describing the elastic-plastic deformation of anisotropic heterogeneous crystalline matter is presented and compared with experiments.
1,573 citations
01 Jan 2011
509 citations
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TL;DR: Sequence diagrams document the interoperability of the analysis classes for solving nonlinear finite-element equations, demonstrating that object composition with design patterns provides a general approach to developing and refactoring nonlinear infinite-element software.
Abstract: Object composition offers significant advantages over class inheritance to develop a flexible software architecture for finite-element analysis. Using this approach, separate classes encapsulate fu...
490 citations
TL;DR: In this article, a review of multiscale methods for modeling mechanical and thermomechanical responses of composites is presented, both at the material level and at the structural analysis level.
Abstract: Various multiscale methods are reviewed in the context of modelling mechanical and thermomechanical responses of composites. They are developed both at the material level and at the structural analysis level, considering sequential or integrated kinds of approaches. More specifically, such schemes like periodic homogenization or mean field approaches are compared and discussed, especially in the context of non linear behaviour. Some recent developments are considered, both in terms of numerical methods (like FE2) and for more analytical approaches based on Transformation Field Analysis, considering both the homogenization and relocalisation steps in the multiscale methodology. Several examples are shown.
489 citations
TL;DR: Robotic materials can enable smart composites that autonomously change their shape, stiffness, or physical appearance in a fully programmable way, extending the functionality of classical “smart materials.”
Abstract: BACKGROUND The tight integration of sensing, actuation, and computation that biological systems exhibit to achieve shape and appearance changes (like the cuttlefish and birds in flight), adaptive load support (like the banyan tree), or tactile sensing at very high dynamic range (such as the human skin) has long served as inspiration for engineered systems. Artificial materials with such capabilities could enable airplane wings and vehicles with the ability to adapt their aerodynamic profile or camouflage in the environment, bridges and other civil structures that could detect and repair damages, or robotic skin and prosthetics with the ability to sense touch and subtle textures. The vision for such materials has been articulated repeatedly in science and fiction (“programmable matter”) and periodically has undergone a renaissance with the advent of new enabling technology such as fast digital electronics in the 1970s and microelectromechanical systems in the 1990s. ADVANCES Recent advances in manufacturing, combined with the miniaturization of electronics that has culminated in providing the power of a desktop computer of the 1990s on the head of a pin, is enabling a new class of “robotic” materials that transcend classical composite materials in functionality. Whereas state-of-the-art composites are increasingly integrating sensors and actuators at high densities, the availability of cheap and small microprocessors will allow these materials to function autonomously. Yet, this vision requires the tight integration of material science, computer science, and other related disciplines to make fundamental advances in distributed algorithms and manufacturing processes. Advances are currently being made in individual disciplines rather than system integration, which has become increasingly possible in recent years. For example, the composite materials community has made tremendous advances in composites that integrate sensing for nondestructive evaluation, and actuation (for example, for shape-changing airfoils), as well as their manufacturing. At the same time, computer science has created an entire field concerned with distributed algorithms to collect, process, and act upon vast collections of information in the field of sensor networks. Similarly, manufacturing has been revolutionized by advances in three-dimensional (3D) printing, as well as entirely new methods for creating complex structures from unfolding or stretching of patterned 2D composites. Finally, robotics and controls have made advances in controlling robots with multiple actuators, continuum dynamics, and large numbers of distributed sensors. Only a few systems have taken advantage of these advances, however, to create materials that tightly integrate sensing, actuation, computation, and communication in a way that allows them to be mass-produced cheaply and easily. OUTLOOK Robotic materials can enable smart composites that autonomously change their shape, stiffness, or physical appearance in a fully programmable way, extending the functionality of classical “smart materials.” If mass-produced economically and available as a commodity, robotic materials have the potential to add unprecedented functionality to everyday objects and surfaces, enabling a vast array of applications ranging from more efficient aircraft and vehicles, to sensorial robotics and prosthetics, to everyday objects like clothing and furniture. Realizing this vision requires not only a new level of interdisciplinary collaboration between the engineering disciplines and the sciences, but also a new model of interdisciplinary education that captures both the disciplinary breadth of robotic materials and the depth of individual disciplines.
480 citations
Cites background or methods from "The Finite Element Method for Solid..."
...More complex geometries, such as those found in real world structures, require computationally intensive numerical modeling approaches, such as finite element methods (FEM) [179]....
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...The primary drawback of FEM is the computational requirements are very large: the physical dimensions of meshes must be small enough to effectively model small defects, while the number of meshes must be sufficient to cover the entire structure under investigation....
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...world structures, require computationally intensive numerical modeling approaches, such as finite element methods (FEM) [179]....
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...For structural health monitoring, the undamaged state of a structure may be simulated using FEM, and the behavior of the actual structure can be compared to this simulation to determine the presence of defects or damage....
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...Finite element method (FEM) [179] is a powerful and common approach which involves generating a mesh which approximates the structure of interest, approximating the physical response of each element in the mesh, and enforcing continuity of the physical behavior between meshes at their boundary....
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