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Filip C Filippou - One of the best experts on this subject based on the ideXlab platform.
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inelastic axial flexure shear coupling in a Mixed Formulation beam finite element
International Journal of Non-linear Mechanics, 2009Co-Authors: Afsin Saritas, Filip C FilippouAbstract:Abstract In this paper a beam element that accounts for inelastic axial-flexure–shear coupling is presented. The mathematical model is derived from a three-field variational form. The finite element approximation for the beam uses shape functions for section forces that satisfy equilibrium and discontinuous section deformations along the beam. No approximation for the beam displacement field is necessary in the Formulation. The coupling of the section forces is achieved through the numerical integration of an inelastic multi-axial material model over the cross-section. The proposed element is free from shear-locking. Examples confirm the accuracy and numerical robustness of the proposed element and showcase the interaction between axial force, shear, and bending moment.
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Mixed Formulation of nonlinear steel concrete composite beam element
Journal of Structural Engineering-asce, 2000Co-Authors: Ashraf Ayoub, Filip C FilippouAbstract:This paper presents an inelastic beam element for the analysis of steel-concrete girders with partial composite action under monotonic and cyclic loads. The element is derived from a two-field Mixed Formulation with independent approximation of internal forces and transverse displacements. The nonlinear response of the steel and concrete component of the girder is based on the section discretization into fibers with uniaxial hysteretic material models for the constituent materials. The partial interaction between concrete deck and steel girder through shear connectors is accounted for by an interface model with distributed force transfer charac- teristics. A direct state determination algorithm for the implementation of the composite element in a general purpose nonlinear analysis program is presented, and the stability characteristics of the algorithm are discussed in conjunction with the selection of appropriate force and displacement interpolation functions. The validity of the model is established by correlation of analytical results with experimental evidence. Numerical studies are used to compare the model with the classical displacement Formulation. These studies confirm the superiority of the proposed model in modeling composite girders under monotonic and cyclic loads that induce stiffness deterioration and strength softening.
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Mixed Formulation of bond slip problems under cyclic loads
Journal of Structural Engineering-asce, 1999Co-Authors: Ashraf Ayoub, Filip C FilippouAbstract:The stress transfer mechanism between reinforcing steel and surrounding concrete through bond and the resulting slip plays an important role in the hysteretic behavior of reinforced concrete structures. Earlier models of the stress transfer problem were based on a displacement Formulation. Recent models, however, have demonstrated the significant advantages of a flexibility Formulation on account of its accuracy and numerical stability under large inelastic strains in the reinforcing steel and bond damage in the surrounding concrete. This paper presents a critical evaluation of existing anchored reinforcing bar models and proposes a new model based on a two-field Mixed Formulation in which independent interpolation functions are used for the relative slip and the reinforcing steel forces. The advantages of this approach over existing models are assessed by numerical studies of anchored reinforcing bars under monotonic loads. The accuracy of the proposed model is established by correlation of analytical results with experimental data of an anchored reinforcing bar under severe cyclic loading.
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Mixed Formulation of nonlinear beam finite element
Computers & Structures, 1996Co-Authors: Enrico Spacone, V Ciampi, Filip C FilippouAbstract:Recent studies show that beam finite elements that enforce equilibrium rather than compatibility along the element are better suited for the description of the nonlinear behavior of frame elements. This is particularly true for elements that exhibit loss of strength and stiffness under monotonic and cyclic loads. Existing Formulations, however, fail to define a consistent way of implementing the force method in the context of imposed kinematic, rather than static, boundary conditions, as is the case for element models in a standard finite element program. This paper derives the general Formulation of a beam finite element from a Mixed approach which points the way to the consistent numerical implementation of the element state determination in the context of a standard finite element program. The element state determination centers on a new iterative solution algorithm that is based on residual deformations rather than residual forces at the section and element level. Equilibrium is enforced in a strict sense along the element, while the section constitutive relation is satisfied within a specified tolerance when the algorithm converges. The proposed algorithm is general and can be used with any section constitutive relation.
Ashraf Ayoub - One of the best experts on this subject based on the ideXlab platform.
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Mixed Formulation for geometric and material nonlinearity of shear critical reinforced concrete columns
Engineering Structures, 2021Co-Authors: Dipankar Das, Ashraf AyoubAbstract:Abstract This study presents a new beam element Formulation following a Hellinger-Reissner variational principle for shear critical reinforced concrete members, and considering large displacement and rotation effects. The corotational Formulation is used to describe the large displacement at the element nodal level and degenerated Green-Lagrange strain measures are used at the basic element level. A new displacement shape function has been developed considering section kinematics and compatibility conditions to satisfy stability criteria. New explicit equations for the internal geometric stiffness matrix to consider large deformation effect has been developed. A robust state determination algorithm for the large deformation Mixed-based Formulation is proposed. The Timoshenko beam theory has been adopted to consider shear deformations in deriving the section kinematics equations. The multi-axial stress state in reinforced concrete fibre has been simulated through the fixed crack smeared softened membrane model. The developed shear fibre beam element is capable of accurately reproducing the experimentally-observed large displacement effect on the post-peak shear strength degradation in the softening region. The accuracy and efficiency of the Mixed-based Formulation was evaluated by examining the responses at local and global levels for both monotonic and reverse cyclic loading conditions along with the process of reproducing experimentally-observed failure modes.
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nonlinear analysis of reinforced concrete beam columns with bond slip
Journal of Engineering Mechanics-asce, 2006Co-Authors: Ashraf AyoubAbstract:This paper presents a new model for nonlinear analysis of reinforced concrete beam–columns with bond–slip. The model is derived from a two-field Mixed Formulation with independent approximation of forces and displacements. The state determination algorithm for the implementation of the model in a general purpose nonlinear finite-element analysis program is presented and its stability characteristics are discussed. Both, bond–slip and pull-out effects, are represented in the model. The paper concludes with a correlation study to investigate the validity of the model. The study confirmed the accuracy of the model in representing global and particularly local parameters.
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Mixed Formulation of nonlinear steel concrete composite beam element
Journal of Structural Engineering-asce, 2000Co-Authors: Ashraf Ayoub, Filip C FilippouAbstract:This paper presents an inelastic beam element for the analysis of steel-concrete girders with partial composite action under monotonic and cyclic loads. The element is derived from a two-field Mixed Formulation with independent approximation of internal forces and transverse displacements. The nonlinear response of the steel and concrete component of the girder is based on the section discretization into fibers with uniaxial hysteretic material models for the constituent materials. The partial interaction between concrete deck and steel girder through shear connectors is accounted for by an interface model with distributed force transfer charac- teristics. A direct state determination algorithm for the implementation of the composite element in a general purpose nonlinear analysis program is presented, and the stability characteristics of the algorithm are discussed in conjunction with the selection of appropriate force and displacement interpolation functions. The validity of the model is established by correlation of analytical results with experimental evidence. Numerical studies are used to compare the model with the classical displacement Formulation. These studies confirm the superiority of the proposed model in modeling composite girders under monotonic and cyclic loads that induce stiffness deterioration and strength softening.
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Mixed Formulation of bond slip problems under cyclic loads
Journal of Structural Engineering-asce, 1999Co-Authors: Ashraf Ayoub, Filip C FilippouAbstract:The stress transfer mechanism between reinforcing steel and surrounding concrete through bond and the resulting slip plays an important role in the hysteretic behavior of reinforced concrete structures. Earlier models of the stress transfer problem were based on a displacement Formulation. Recent models, however, have demonstrated the significant advantages of a flexibility Formulation on account of its accuracy and numerical stability under large inelastic strains in the reinforcing steel and bond damage in the surrounding concrete. This paper presents a critical evaluation of existing anchored reinforcing bar models and proposes a new model based on a two-field Mixed Formulation in which independent interpolation functions are used for the relative slip and the reinforcing steel forces. The advantages of this approach over existing models are assessed by numerical studies of anchored reinforcing bars under monotonic loads. The accuracy of the proposed model is established by correlation of analytical results with experimental data of an anchored reinforcing bar under severe cyclic loading.
Emmanuel Creuse - One of the best experts on this subject based on the ideXlab platform.
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a posteriori error estimation for the dual Mixed finite element method for the p laplacian in a polygonal domain
Computer Methods in Applied Mechanics and Engineering, 2007Co-Authors: Mohamed Farhloul, Emmanuel Creuse, L PaquetAbstract:For the discrete solution of the dual Mixed Formulation for the p -Laplace equation, we define two residues R and r . Then we bound the norm of the errors on the two unknowns in terms of the norms of these two residues. Afterwards, we bound the norms of these two residues by functions of two error estimators whose expressions involve at the very most the datum and the computed quantities. We next explain how the discretized dual Mixed Formulation is hybridized and solved. We close our paper by numerical tests for p=1.8 p = 1.8 and p=3 p = 3 firstly to corroborate the orders of convergence established by Farhloul and Manouzi [M. Farhloul, H. Manouzi, On a Mixed finite element method for the p -Laplacian, Canadian Applied Mathematics Quarterly 8 (2000) 67–78], and secondly to experimentally verify the reliability of our a posteriori error estimates.
L Paquet - One of the best experts on this subject based on the ideXlab platform.
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a priori error estimation for the dual Mixed finite element method of the elastodynamic problem in a polygonal domain ii
Journal of Computational and Applied Mathematics, 2011Co-Authors: L Boulaajine, Mohamed Farhloul, L PaquetAbstract:In this paper we analyze a new dual Mixed Formulation of the elastodynamic system in polygonal domains by using an implicit scheme for the time discretization. After the analysis of stability of the fully discrete scheme, L^~ in time, L^2 in space a priori error estimates for the approximation of the displacement, the strain, the pressure and the rotational are derived. Numerical tests are presented which confirm our theoretical results.
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a posteriori error estimation for the dual Mixed finite element method for the p laplacian in a polygonal domain
Computer Methods in Applied Mechanics and Engineering, 2007Co-Authors: Mohamed Farhloul, Emmanuel Creuse, L PaquetAbstract:For the discrete solution of the dual Mixed Formulation for the p -Laplace equation, we define two residues R and r . Then we bound the norm of the errors on the two unknowns in terms of the norms of these two residues. Afterwards, we bound the norms of these two residues by functions of two error estimators whose expressions involve at the very most the datum and the computed quantities. We next explain how the discretized dual Mixed Formulation is hybridized and solved. We close our paper by numerical tests for p=1.8 p = 1.8 and p=3 p = 3 firstly to corroborate the orders of convergence established by Farhloul and Manouzi [M. Farhloul, H. Manouzi, On a Mixed finite element method for the p -Laplacian, Canadian Applied Mathematics Quarterly 8 (2000) 67–78], and secondly to experimentally verify the reliability of our a posteriori error estimates.
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refined Mixed finite element method for the elasticity problem in a polygonal domain
Numerical Methods for Partial Differential Equations, 2002Co-Authors: Mohamed Farhloul, L PaquetAbstract:The purpose of this article is to study a Mixed Formulation of the elasticity problem in plane polygonal domains and its numerical approximation. In this Mixed Formulation the strain tensor is introduced as a new unknown and its symmetry is relaxed by a Lagrange multiplier, which is nothing else than the rotation. Because of the corner points, the displacement field is not regular in general in the vicinity of the vertices but belongs to some weighted Sobolev space. Using this information, appropriate refinement rules are imposed on the family of triangulations in order to recapture optimal error estimates. Moreover, uniform error estimates in the Lame coefficient λ are obtained for λ large. © 2002 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 18: 323–339, 2002; Published online in Wiley InterScience (www.interscience.wiley.com). DOI 10.1002/num.10009
Gabriel N Gatica - One of the best experts on this subject based on the ideXlab platform.
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a priori and a posteriori error analyses of a pseudostress based Mixed Formulation for linear elasticity
Computers & Mathematics With Applications, 2016Co-Authors: Gabriel N Gatica, Luis F Gatica, Filander A SequeiraAbstract:In this paper we present the a priori and a posteriori error analyses of a non-standard Mixed finite element method for the linear elasticity problem with non-homogeneous Dirichlet boundary conditions. More precisely, the approach introduced here is based on a simplified interpretation of the pseudostress-displacement Formulation originally proposed in Arnold and Falk (1988), which does not require symmetric tensor spaces in the finite element discretization. In addition, physical quantities such as the stress, the strain tensor of small deformations, and the rotation, are computed through a simple postprocessing in terms of the pseudostress variable. Furthermore, we also introduce a second element-by-element postprocessing formula for the stress, which yields an optimally convergent approximation of this unknown with respect to the broken H ( div ) -norm. We apply the classical Babuska-Brezzi theory to prove that the corresponding continuous and discrete schemes are well-posed. In particular, Raviart-Thomas spaces of order k ? 0 for the pseudostress and piecewise polynomials of degree ? k for the displacement can be utilized. Moreover, we remark that in the 3D case the number of unknowns behaves approximately as 9 times the number of elements (tetrahedra) of the triangulation when k = 0 . This factor increases to 12.5 when one uses the classical PEERS. Next, we derive a reliable and efficient residual-based a posteriori error estimator for the Mixed finite element scheme. Finally, several numerical results illustrating the performance of the method, confirming the theoretical properties of the estimator, and showing the expected behaviour of the associated adaptive algorithm, are provided.
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a residual based a posteriori error estimator for a fully Mixed Formulation of the stokes darcy coupled problem
Computer Methods in Applied Mechanics and Engineering, 2011Co-Authors: Gabriel N Gatica, Ricardo Oyarzua, Franciscojavier SayasAbstract:Abstract In this paper we develop an a posteriori error analysis of a new fully Mixed finite element method for the coupling of fluid flow with porous media flow in 2D. Flows are governed by the Stokes and Darcy equations, respectively, and the corresponding transmission conditions are given by mass conservation, balance of normal forces, and the Beavers–Joseph–Saffman law. We consider dual-Mixed Formulations in both media, which yields the pseudostress and the velocity in the fluid, together with the velocity and the pressure in the porous medium, and the traces of the porous media pressure and the fluid velocity on the interface, as the resulting unknowns. The set of feasible finite element subspaces includes Raviart–Thomas elements of lowest order and piecewise constants for the velocities and pressures, respectively, in both domains, together with continuous piecewise linear elements for the traces. We derive a reliable and efficient residual-based a posteriori error estimator for the coupled problem. The proof of reliability makes use of the global inf–sup condition, Helmholtz decompositions in both media, and local approximation properties of the Clement interpolant and Raviart–Thomas operator. On the other hand, inverse inequalities, the localization technique based on element-bubble and edge-bubble functions, and known results from previous works, are the main tools for proving the efficiency of the estimator. Finally, some numerical results confirming the theoretical properties of this estimator, and illustrating the capability of the corresponding adaptive algorithm to localize the singularities of the solution, are reported.
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a dual dual Mixed Formulation for nonlinear exterior transmission problems
Mathematics of Computation, 2001Co-Authors: Gabriel N Gatica, Salim MeddahiAbstract:We combine a dual-Mixed finite element method with a Dirichletto-Neumann mapping (derived by the boundary integral equation method) to study the solvability and Galerkin approximations of a class of exterior nonlinear transmission problems in the plane. As a model problem, we consider a nonlinear elliptic equation in divergence form coupled with the Laplace equation in an unbounded region of the plane. Our combined approach leads to what we call a dual-dual Mixed variational Formulation since the main operator involved has itself a dual-type structure. We establish existence and uniqueness of solution for the continuous and discrete Formulations, and provide the corresponding error analysis by using Raviart-Thomas elements. The main tool of our analysis is given by a generalization of the usual Babuska-Brezzi theory to a class of nonlinear variational problems with constraints.