1,720,989 research outputs found
From nodal patch schemes to averaged strain elements
No full textIn this paper we present a review of the patch averaged assumed strain element technique, recently proposed in [1, 2, 3] for elastic problems and then developed for structural models such as beams and plates structures with isotropic or composite materials [4, 5, 6]. In this approach a patch averaged strain-displacement matrix is constructed for each node of the mesh, yielding a smoothed representation of strain and stress fields. The appeal of this representation of recovered quantities is clear: recovered quantities does not require to be post-processed in order to obtain unique values at the inter-element interfaces. One of the main novelty of the proposed approach lies in the use of the so-called variational consistency condition: the assumed-strain operators are directly derived by this condition. A comparison with similar averaging techniques shows that usually this condition is used only as an ex post facto test to asses the properties of the assume-strain operators. We detail that the finite element approximation converges uniformly to the exact solution also for problematic cases such as the nearly incompressible case or in the limit of thin plates. The present review investigate also some aspects related to the choice of sampling points to use with the construction of the averaged strain matrix. Upon this choice the proposed technique produces a wide set of elements: accuracy, convergence properties and insensitive response in the presence of shape distortion are among the feature of each proposed element
A nine-node displacement-based finite element for Reissner-Mindlin plates based on an improved formulation of the NIPE approach
No full textThe nodally integrated plate element formulation is an assumed strain finite element technique for shear deformable plates that enforce weakly the balance and the kinematic equations. The strain-displacement operators are derived via nodal integration satisfying a priori the kinematic weighted residual statement. The present work analyzes the NIPE technique, including the new element, by testing thoughtfully the sensitivity of the elements to severe geometry distortions. We propose an improvement that confers robustness to all element shapes developed by the NIPE formulation. We present also a new nine-node NIP element configuration. The new nine-node element uses bi-quadratic interpolations of the transverse displacement and rotations and is computed by means of a nine-node quadrature rule. A brief review of the improved triangular and quadrangular NIPEs is reported for elastic plate analyses. A few challenging benchmarks carried out on extreme distorted meshes illustrate the performance of the introduced NIP-Q9 element. We detail that the new NIPE formulation confers insensitivity to extreme distortions for the quadratic quadrilateral element and allows to solve for severe distortion with the NIPE family
Displacement-based finite elements with nodal integration for Reissner-Mindlin plates
No full textAn assumed-strain finite element technique is presented for shear-deformable (Reissner-Mindlin) plates. The weighted residual method (reminiscent of the strain-displacement functional) is used to enforce weakly the balance equation with the natural boundary condition and, separately, the kinematic equation (the strain-displacement relationship). The a priori satisfaction of the kinematic weighted residual serves as a condition from which strain-displacement operators are derived via nodal integration, for linear triangles, and quadrilaterals, and also for quadratic triangles. The degrees of freedom are only the primitive variables: transverse displacements and rotations at the nodes. A straightforward constraint count can partially explain the insensitivity of the resulting finite element models to locking in the thin-plate limit. We also construct an energy-based argument for the ability of the present formulation to converge to the correct deflections in the limit of the thickness approaching zero. Examples are used to illustrate the performance with particular attention to the sensitivity to element shape and shear locking
Assumed strain nodally integrated hexahedral finite element formulation for elastoplastic applications
No full textIn this work, a linear hexahedral element based on an assumed strain finite element technique is presented for the solution of plasticity problems. The element stems from the Nodally Integrated Continuum Element (NICE) formulation and its extensions. Assumed gradient operators are derived via nodal integration from the kinematic-weighted residual; the degrees of freedom are only the displacements at the nodes. The adopted constitutive model is the classical associative von Mises plasticity model with isotropic and kinematic hardening; in particular, a double-step midpoint integration algorithm is adopted for the integration and solution of the relevant nonlinear evolution equations. Efficiency of the proposed method is assessed through simple benchmark problems and comparison with reference solutions
A displacement-based finite element formulation for the analysis of laminated composite plates
No full textThis paper presents the nodally integrated plate element (NIPE) formulation for the analysis of laminated composite plates based on the first-order shear deformation theory. The nodally integrated approach aims at providing smoothed derivative quantities by constructing nodal strain-displacement operators. Within this framework a new family of elements for plates with general monoclinic layers is developed: the strain-displacement operators are derived via nodal integration for linear triangles and quadrilateral elements. The degrees of freedom are only the primitive variables: displacements and rotations at the nodes. The NIPEs are locking-free elements, exhibit little sensitivity to geometric distortions and can be readily implemented into existing finite element codes. The efficiency of the proposed variational formulation is proved whereas effectiveness and convergence of the proposed finite elements are confirmed through several numerical applications. Finally, numerical results are compared with the corresponding analytical solutions as well as to other finite-element solutions
Linear tetrahedral element for problems of plastic deformation
No full textLinear tetrahedra perform poorly in problems with plasticity, nearly incompressible materials, and in bending. While higher-order tetrahedra can cure or alleviate some of these weaknesses, in many situations low-order tetrahedral elements would be preferable to quadratic tetrahedral elements: e.g. for contact problems or fluid-structure interaction simulations. Therefore, a low-order tetrahedron that would look on the outside as a regular four-node tetrahedron, but that would possess superior accuracy is desirable. An assumed-strain, nodally integrated, four-node tetrahedral element is presented (NICE-T4). Several numerical benchmarks are provided showing its robust performance in conjunction with material nonlinearity in the form of von Mises plasticity. In addition we compare the computational cost of the nodally integrated NICE-T4 with the isoparametric quadratic tetrahedron. Because of the reduced number of quadrature points, the NICE-T4 element is competitive in nonlinear analyses with complex material models
Patch-averaged assumed strain finite elements for stress analysis
No full textA finite element model for linear-elastic small deformation problems is presented. The formulation is based on a weighted residual that requires a priori the satisfaction of the kinematic equation. In this approach, an averaged strain-displacement matrix is constructed for each node of the mesh by defining an appropriate patch of elements, yielding a smooth representation of strain and stress fields. Connections with traditional and similar procedure are explored. Linear quadrilateral four-node and linear hexahedral eight-node elements are derived. Various numerical tests show the accuracy and convergence properties of the proposed elements in comparison with extant finite elements and analytic solutions. Specific examples are also included to illustrate the ability to resist numerical locking in the incompressible limit and insensitive response in the presence of shape distortion. Furthermore, the numerical inf-sup test is applied to a selection of problems to show the stability of the present formulation
Assumed-strain finite element technique for accurate modelling of plasticity problems
Full text linkIn this work a linear hexahedral element based on an assumed-strain finite element technique is presented for the solution of plasticity problems. The element stems from the NICE formulation and its extensions. Assumed gradient operators are derived via nodal integration from the kinematic-weighted residual; the degrees of freedom are only the displacements at the nodes. The adopted constitutive model is the classical associative von-Mises plasticity model with isotropic and kinematic hardening; in particular a double- step midpoint integration algorithm is adopted for the integration and solution of the relevant nonlinear evolution equations. Efficiency of the proposed method is assessed through simple benchmark problem and comparison with reference solutions
Going Beyond Counting First Authors in Author Co-citation Analysis
Full text linkThe present study examines one of the fundamental aspects of author co-citation analysis (ACA) - the way co-citation
counts are defined. Co-citation counting provides the data on which all subsequent statistical analyses and mappings
are based, and we compare ACA results based on two different types of co-citation counting - the traditional type that
only counts the first one among a cited work's authors on the one hand and a non-traditional type that takes into
account the first 5 authors of a cited work on the other hand. Results indicate that the picture produced through this non-traditional author co-citation counting contains more coherent author groups and is therefore considerably clearer. However, this picture represents fewer specialties in the research field being studied than that produced through the traditional first-author co-citation counting when the same number of top-ranked authors is selected and analyzed. Reasons for these effects are discussed
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