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S.p. Vipin - One of the best experts on this subject based on the ideXlab platform.
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New Reduction Factor for cracked multi-planar square hollow section TT-, YT- and KT-joints
Engineering Structures, 2017Co-Authors: Seng Tjhen Lie, S.p. VipinAbstract:Abstract Many existing multi-planar structures such as bridges, buildings and others are fabricated using square hollow section (SHS) members. There are no guidance’s available in the design codes to assess the safety and integrity of these cracked multi-planar SHS joints till date. This paper proposes a new set of equations for determining the Reduction Factor ( F AR ) of cracked multi-planar SHS TT-, YT- and KT-joints. A completely new and robust finite element (FE) mesh generator is developed and it is validated using the experimental test results. Parametric study is carried out for multi-planar SHS joints subjected to axial loading at the brace end. The results reveal that the crack area and the brace to chord width ratio (β) have an important effect on the plastic collapse load of the cracked SHS joints. For a particular β value, the F AR varies up to 4.37% for different values of crack area.
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New Reduction Factor for cracked square hollow section T-joints under axial loading
Journal of Constructional Steel Research, 2015Co-Authors: Seng Tjhen Lie, S.p. VipinAbstract:Abstract This paper proposes a new expression for determining the Reduction Factor ( F AR ) of cracked square hollow section (SHS) joints. The F AR when multiplied with the ultimate strength of uncracked SHS joints, gives the ultimate strength of cracked SHS joints. A completely new and robust finite element mesh generator is developed to generate models for cracked SHS welded joints. The newly developed automatic mesh generator is validated using the experimental results. Parametric study is carried out for SHS joints subjected to axial loading at the brace end. The results reveal that the crack area and the brace to chord width ratio (β) have a significant influence on the ultimate strength of the cracked SHS joints. It is observed that for a particular crack area, the variation of the F AR values is up to 3.29% for different values of β. The results also show that the F AR values calculated using the existing equation for circular hollow section (CHS) joints are conservative in nature with percentage difference of up to 22.67%.
Martin Vohralik - One of the best experts on this subject based on the ideXlab platform.
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an adaptive hp refinement strategy with inexact solvers and computable guaranteed bound on the error Reduction Factor
Computer Methods in Applied Mechanics and Engineering, 2020Co-Authors: Patrik Daniel, Alexandre Ern, Martin VohralikAbstract:In this work we extend our recently proposed adaptive refinement strategy for $hp$-finite element approximations of elliptic problems by taking into account an inexact algebraic solver. Namely, on each level of refinement and on each iteration of an (arbitrary) iterative algebraic solver, we compute guaranteed a posteriori error bounds on the algebraic and the total errors in energy norm. The algebraic error is the difference between the inexact discrete solution obtained by an iterative algebraic solver and the (unavailable) exact discrete solution. On the other hand, the total error stands for the difference between the inexact discrete solution and the (unavailable) exact solution of the partial differential equation. For the algebraic error upper bound, we crucially exploit the whole nested hierarchy of $hp$-finite element spaces created by the adaptive algorithm, whereas the remaining parts of the total error upper and lower bounds are computed using the finest space only. These error bounds allow us to formulate adaptive stopping criteria for the algebraic solver ensuring that the algebraic error does not significantly contribute to the total error. Next, we use the total error bound to mark mesh vertices for refinement via D\"orfler's bulk-chasing criterion. On patches associated with marked vertices only, we solve two separate primal finite element problems with homogeneous Dirichlet (Neumann) boundary conditions, which serve to decide between $h$-, $p$-, or $hp$-refinement. Altogether, we show that these ingredients lead to a computable guaranteed bound on the ratio of the total errors of the inexact approximations between successive refinements (the error Reduction Factor), when the stopping criteria are satisfied. Finally, in a series of numerical experiments, we investigate the practicality of the proposed adaptive solver, the accuracy of our bound on the Reduction Factor, and show that exponential convergence rates are achieved even in the presence of an inexact algebraic solver.
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an adaptive hp refinement strategy with computable guaranteed bound on the error Reduction Factor
Computers & Mathematics With Applications, 2018Co-Authors: Patrik Daniel, Alexandre Ern, Iain Smears, Martin VohralikAbstract:We propose a new practical adaptive refinement strategy for $hp$-finite element approximations of elliptic problems. Following recent theoretical developments in polynomial-degree-robust a posteriori error analysis, we solve two types of discrete local problems on vertex-based patches. The first type involves the solution on each patch of a mixed finite element problem with homogeneous Neumann boundary conditions, which leads to an ${\mathbf H}(\mathrm{div},\Omega)$-conforming equilibrated flux. This, in turn, yields a guaranteed upper bound on the error and serves to mark mesh vertices for refinement via Dorfler's bulk-chasing criterion. The second type of local problems involves the solution, on patches associated with marked vertices only, of two separate primal finite element problems with homogeneous Dirichlet boundary conditions, which serve to decide between $h$-, $p$-, or $hp$-refinement. Altogether, we show that these ingredients lead to a computable guaranteed bound on the ratio of the errors between successive refinements (error Reduction Factor). In a series of numerical experiments featuring smooth and singular solutions, we study the performance of the proposed $hp$-adaptive strategy and observe exponential convergence rates. We also investigate the accuracy of our bound on the Reduction Factor by evaluating the ratio of the predicted Reduction Factor relative to the true error Reduction, and we find that this ratio is in general quite close to the optimal value of one.
Seng Tjhen Lie - One of the best experts on this subject based on the ideXlab platform.
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New Reduction Factor for cracked multi-planar square hollow section TT-, YT- and KT-joints
Engineering Structures, 2017Co-Authors: Seng Tjhen Lie, S.p. VipinAbstract:Abstract Many existing multi-planar structures such as bridges, buildings and others are fabricated using square hollow section (SHS) members. There are no guidance’s available in the design codes to assess the safety and integrity of these cracked multi-planar SHS joints till date. This paper proposes a new set of equations for determining the Reduction Factor ( F AR ) of cracked multi-planar SHS TT-, YT- and KT-joints. A completely new and robust finite element (FE) mesh generator is developed and it is validated using the experimental test results. Parametric study is carried out for multi-planar SHS joints subjected to axial loading at the brace end. The results reveal that the crack area and the brace to chord width ratio (β) have an important effect on the plastic collapse load of the cracked SHS joints. For a particular β value, the F AR varies up to 4.37% for different values of crack area.
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New Reduction Factor for cracked square hollow section T-joints under axial loading
Journal of Constructional Steel Research, 2015Co-Authors: Seng Tjhen Lie, S.p. VipinAbstract:Abstract This paper proposes a new expression for determining the Reduction Factor ( F AR ) of cracked square hollow section (SHS) joints. The F AR when multiplied with the ultimate strength of uncracked SHS joints, gives the ultimate strength of cracked SHS joints. A completely new and robust finite element mesh generator is developed to generate models for cracked SHS welded joints. The newly developed automatic mesh generator is validated using the experimental results. Parametric study is carried out for SHS joints subjected to axial loading at the brace end. The results reveal that the crack area and the brace to chord width ratio (β) have a significant influence on the ultimate strength of the cracked SHS joints. It is observed that for a particular crack area, the variation of the F AR values is up to 3.29% for different values of β. The results also show that the F AR values calculated using the existing equation for circular hollow section (CHS) joints are conservative in nature with percentage difference of up to 22.67%.
Patrik Daniel - One of the best experts on this subject based on the ideXlab platform.
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an adaptive hp refinement strategy with inexact solvers and computable guaranteed bound on the error Reduction Factor
Computer Methods in Applied Mechanics and Engineering, 2020Co-Authors: Patrik Daniel, Alexandre Ern, Martin VohralikAbstract:In this work we extend our recently proposed adaptive refinement strategy for $hp$-finite element approximations of elliptic problems by taking into account an inexact algebraic solver. Namely, on each level of refinement and on each iteration of an (arbitrary) iterative algebraic solver, we compute guaranteed a posteriori error bounds on the algebraic and the total errors in energy norm. The algebraic error is the difference between the inexact discrete solution obtained by an iterative algebraic solver and the (unavailable) exact discrete solution. On the other hand, the total error stands for the difference between the inexact discrete solution and the (unavailable) exact solution of the partial differential equation. For the algebraic error upper bound, we crucially exploit the whole nested hierarchy of $hp$-finite element spaces created by the adaptive algorithm, whereas the remaining parts of the total error upper and lower bounds are computed using the finest space only. These error bounds allow us to formulate adaptive stopping criteria for the algebraic solver ensuring that the algebraic error does not significantly contribute to the total error. Next, we use the total error bound to mark mesh vertices for refinement via D\"orfler's bulk-chasing criterion. On patches associated with marked vertices only, we solve two separate primal finite element problems with homogeneous Dirichlet (Neumann) boundary conditions, which serve to decide between $h$-, $p$-, or $hp$-refinement. Altogether, we show that these ingredients lead to a computable guaranteed bound on the ratio of the total errors of the inexact approximations between successive refinements (the error Reduction Factor), when the stopping criteria are satisfied. Finally, in a series of numerical experiments, we investigate the practicality of the proposed adaptive solver, the accuracy of our bound on the Reduction Factor, and show that exponential convergence rates are achieved even in the presence of an inexact algebraic solver.
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an adaptive hp refinement strategy with computable guaranteed bound on the error Reduction Factor
Computers & Mathematics With Applications, 2018Co-Authors: Patrik Daniel, Alexandre Ern, Iain Smears, Martin VohralikAbstract:We propose a new practical adaptive refinement strategy for $hp$-finite element approximations of elliptic problems. Following recent theoretical developments in polynomial-degree-robust a posteriori error analysis, we solve two types of discrete local problems on vertex-based patches. The first type involves the solution on each patch of a mixed finite element problem with homogeneous Neumann boundary conditions, which leads to an ${\mathbf H}(\mathrm{div},\Omega)$-conforming equilibrated flux. This, in turn, yields a guaranteed upper bound on the error and serves to mark mesh vertices for refinement via Dorfler's bulk-chasing criterion. The second type of local problems involves the solution, on patches associated with marked vertices only, of two separate primal finite element problems with homogeneous Dirichlet boundary conditions, which serve to decide between $h$-, $p$-, or $hp$-refinement. Altogether, we show that these ingredients lead to a computable guaranteed bound on the ratio of the errors between successive refinements (error Reduction Factor). In a series of numerical experiments featuring smooth and singular solutions, we study the performance of the proposed $hp$-adaptive strategy and observe exponential convergence rates. We also investigate the accuracy of our bound on the Reduction Factor by evaluating the ratio of the predicted Reduction Factor relative to the true error Reduction, and we find that this ratio is in general quite close to the optimal value of one.
Vipin, Sukumara Pillai - One of the best experts on this subject based on the ideXlab platform.
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New Reduction Factor for Cracked Square hollow section K-joints
'Elsevier BV', 2018Co-Authors: Vipin, Sukumara Pillai, Kolios Athanasios, Lie S. T., Wang L.Abstract:Cracks are commonly observed at the hot spot stress location of tubular joints and it can be due to fatigue, accidental damage or corrosion. As a consequence, the plastic collapse load (Pc) of the tubular joints is reduced, and hence it is necessary to produce design guidance which can safely be used to estimate the static residual strength of cracked tubular structures in practice. This paper proposes a new expression for determining the Reduction Factor (FAR) of cracked square hollow section (SHS) K-joints. A completely new and robust finite element mesh generator which is validated using the full scale experimental test results is used for the parametric study to propose the new FAR expressions for cracked SHS K-joints. The crack area and the brace to chord width ratio (β) are shown to have the most profound effect on the Pc load of cracked SHS K-joints. For a given value of crack area, the variation of the FAR values is up to 3.6% for different values of β. Furthermore, the FAR values calculated using the existing equation given in the latest BS 7910:2013 + A1:2015 for circular hollow section (CHS) joints are revealed to be conservative up to 23.5%
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New Reduction Factor for cracked multi-planar square hollow section TT-, YT- and KT-joints
2017Co-Authors: Lie, Seng Tjhen, Vipin, Sukumara Pillai, Li TaoAbstract:Many existing multi-planar structures such as bridges, buildings and others are fabricated using square hollow section (SHS) members. There are no guidance’s available in the design codes to assess the safety and integrity of these cracked multi-planar SHS joints till date. This paper proposes a new set of equations for determining the Reduction Factor (FAR) of cracked multi-planar SHS TT-, YT- and KT-joints. A completely new and robust finite element (FE) mesh generator is developed and it is validated using the experimental test results. Parametric study is carried out for multi-planar SHS joints subjected to axial loading at the brace end. The results reveal that the crack area and the brace to chord width ratio (β) have an important effect on the plastic collapse load of the cracked SHS joints. For a particular β value, the FAR varies up to 4.37% for different values of crack area.Accepted versio
