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Wyniki wyszukiwania dla: COSSERAT CONTINUUM
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On Non-holonomic Boundary Conditions within the Nonlinear Cosserat Continuum
PublikacjaWithin the framework of the nonlinear micropolar elastic continuum we discuss non-holonomic kinematic boundary conditions. By non-holonomic boundary conditions we mean linear relations between virtual displacements and virtual rotations given on the boundary. Such boundary conditions can be used for modelling of complex material interactions in the vicinity of the boundaries and interfaces.
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Non-standard contact conditions in generalized continua: microblock contact model for a Cosserat body
PublikacjaGeneralized continuum theories involve non-standard boundary conditions that are associated with the additional kinematic variables introduced in those theories, e.g., higher gradients of the displacement field or additional kinematic degrees of freedom. Accordingly, formulation of a contact problem for such a continuum necessarily requires that adequate contact conditions are formulated for the additional kinematic variables and/or...
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On rotational instability within the nonlinear six-parameter shell theory
PublikacjaWithin the six-parameter nonlinear shell theory we analyzed the in-plane rotational instability which oc- curs under in-plane tensile loading. For plane deformations the considered shell model coincides up to notations with the geometrically nonlinear Cosserat continuum under plane stress conditions. So we con- sidered here both large translations and rotations. The constitutive relations contain some additional mi- cropolar parameters...
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A Nonlinear Model of a Mesh Shell
PublikacjaFor a certain class of elastic lattice shells experiencing finite deformations, a continual model using the equations of the so-called six-parameter shell theory has been proposed. Within this model, the kinematics of the shell is described using six kinematically independent scalar degrees of freedom — the field of displacements and turns, as in the case of the Cosserat continuum, which gives reason to call the model under consideration...
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Modeling of Composite Shells in 6-Parameter Nonlinear Theory with Drilling Degree of Freedom
PublikacjaWithin the framework of a 6-parameter nonlinear shell theory, with strain measures of Cosserat type, constitutive relations are proposed for thin elastic composite shells. The material law is expressed in terms of five engineering constants of classical anisotropic continuum plus an additional parameter accounting for drilling stiffness. The theory allows for unlimited displacements and rotations. A number of examples are presented...
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On the exact equilibrium conditions of irregular shells reinforced by beams along the junctions
PublikacjaThe exact, resultant equilibrium conditions for irregular shells reinforced by beams along the junctions are formulated. The equilibrium conditions are derived by performing direct integration of the global equilibrium conditions of continuum mechanics. New, exact resultant static continuity conditions along the singular curve modelling reinforced junction are presented. The results do not depend on shell thickness, internal through-the-thickness...
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Two- and three-dimensional elastic networks with rigid junctions: modeling within the theory of micropolar shells and solids
PublikacjaFor two- and three-dimensional elastic structures made of families of flexible elastic fibers undergoing finite deformations, we propose homogenized models within the micropolar elasticity. Here we restrict ourselves to networks with rigid connections between fibers. In other words, we assume that the fibers keep their orthogonality during deformation. Starting from a fiber as the basic structured element modeled by the Cosserat...
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On FEM analysis of Cosserat-type stiffened shells. Static and stability linear analysis
PublikacjaThe present research investigates the theory and numerical analysis of shells stiffened with beams in the framework based on the geometrically exact theories of shells and beams. Shell’s and beam’s kinematics are described by the Cosserat surface and the Cosserat rod respectively, which are consistent including deformation and strain measures. A FEM approximation of the virtual work principle leads to the conforming shell and beam...
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Structural response of existing spatial truss roof construction based on Cosserat rod theory
PublikacjaPaper presents the application of the Cosserat rod theory and newly developed associated finite elements code as the tools that support in the expert-designing engineering practice. Mechanical principles of the 3D spatially curved rods, dynamics (statics) laws, principle of virtual work are discussed. Corresponding FEM approach with interpolation and accumulation techniques of state variables are shown that enable the formulation...
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Robust four-node elements based on Hu–Washizu principle for nonlinear analysis of Cosserat shells
PublikacjaMixed 4-node shell elements with the drilling rotation and Cosserat-type strain measures based onthe three-field Hu–Washizu principle are proposed. In the formulation, apart from displacement and rotationfields, both strain and stress resultant fields are treated as independent. The elements are derived in the frame-work of a general nonlinear 6-parameter shell theory dedicated to the analysis of multifold irregular shells.The...
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Nonlinear free and forced vibrations of a dielectric elastomer-based microcantilever for atomic force microscopy
PublikacjaThe majority of atomic force microcode (AFM) probes work based on piezoelectric actuation. However, some undesirable phenomena such as creep and hysteresis may appear in the piezoelectric actuators that limit their applications. This paper proposes a novel AFM probe based on dielectric elastomer actuators (DEAs). The DE is modeled via the use of a hyperelastic Cosserat model. Size effects and geometric nonlinearity are included...
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On Dynamic Extension of a Local Material Symmetry Group for Micropolar Media
PublikacjaFor micropolar media we present a new definition of the local material symmetry group considering invariant properties of the both kinetic energy and strain energy density under changes of a reference placement. Unlike simple (Cauchy) materials, micropolar media can be characterized through two kinematically independent fields, that are translation vector and orthogonal microrotation tensor. In other words, in micropolar continua...