Chandrashekhar Jog - Academia.edu (original) (raw)

Papers by Chandrashekhar Jog

Research paper thumbnail of A Monolithic Finite Element Formulation for Magnetohydrodynamics Involving a Compressible Fluid

Fluids, 2022

This work develops a new monolithic finite-element-based strategy for magnetohydrodynamics (MHD) ... more This work develops a new monolithic finite-element-based strategy for magnetohydrodynamics (MHD) involving a compressible fluid based on a continuous velocity–pressure formulation. The entire formulation is within a nodal finite element framework, and is directly in terms of physical variables. The exact linearization of the variational formulation ensures a quadratic rate of convergence in the vicinity of the solution. Both steady-state and transient formulations are presented for two- and three-dimensional flows. Several benchmark problems are presented, and comparisons are carried out against analytical solutions, experimental data, or against other numerical schemes for MHD. We show a good coarse-mesh accuracy and robustness of the proposed strategy, even at high Hartmann numbers.

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Research paper thumbnail of Topology Design of Three-Dimensional Structures Using Hybrid Finite Elements

Solid Mechanics and Its Applications

ABSTRACT Conventional three-dimensional isoparametric elements are susceptible to problems of loc... more ABSTRACT Conventional three-dimensional isoparametric elements are susceptible to problems of locking when used to model plate/shell geometries or when the meshes are distorted etc. Hybrid elements that are based on a two-field variational formulation are immune to most of these problems, and hence can be used to efficiently model both “chunky” three-dimensional and plate/shell type structures. Thus, only one type of element can be used to model “all” types of structures, and also allows us to use a standard dual algorithm for carrying out the topology optimization of the structure. We also address the issue of manufacturability of the designs.

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Research paper thumbnail of A distributed environment for run-time visualization and application steering in computational mechanics

Computing Systems in Engineering, 1992

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Research paper thumbnail of Mixed finite elements for electromagnetic analysis

Computers & Mathematics with Applications, 2014

ABSTRACT The occurrence of spurious solutions is a well-known limitation of the standard nodal fi... more ABSTRACT The occurrence of spurious solutions is a well-known limitation of the standard nodal finite element method when applied to electromagnetic problems. The two commonly used remedies that are used to address this problem are (i) The addition of a penalty term with the penalty factor based on the local dielectric constant, and which reduces to a Helmholtz form on homogeneous domains (regularized formulation); (ii) A formulation based on a vector and a scalar potential. Both these strategies have some shortcomings. The penalty method does not completely get rid of the spurious modes, and both methods are incapable of predicting singular eigenvalues in non-convex domains. Some non-zero spurious eigenvalues are also predicted by these methods on non-convex domains. In this work, we develop mixed finite element formulations which predict the eigenfrequencies (including their multiplicities) accurately, even for nonconvex domains. The main feature of the proposed mixed finite element formulation is that no ad-hoc terms are added to the formulation as in the penalty formulation, and the improvement is achieved purely by an appropriate choice of finite element spaces for the different variables. We show that the formulation works even for inhomogeneous domains where ‘double noding’ is used to enforce the appropriate continuity requirements at an interface. For two-dimensional problems, the shape of the domain can be arbitrary, while for the three-dimensional ones, with our current formulation, only regular domains (which can be nonconvex) can be modeled. Since eigenfrequencies are modeled accurately, these elements also yield accurate results for driven problems.

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Research paper thumbnail of A Note on Boundary Conditions

Foundations and Applications of Mechanics

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Research paper thumbnail of Some Results in n-Dimensional Euclidean Spaces

Foundations and Applications of Mechanics

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Research paper thumbnail of Oblate Spheroidal Coordinate System

Foundations and Applications of Mechanics

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Research paper thumbnail of Nonlinear Elasticity

Foundations and Applications of Mechanics

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Research paper thumbnail of Constitutive Equations

Foundations and Applications of Mechanics

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Research paper thumbnail of Introduction to Tensors

Foundations and Applications of Mechanics

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Research paper thumbnail of A new approach to variable-topology shape design using a constraint on perimeter

Structural Optimization, 1996

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Research paper thumbnail of Modal projections for synchronous rotor whirl

Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences, 2008

We consider the synchronous whirl of arbitrary axisymmetric rotors supported on rigid bearings. P... more We consider the synchronous whirl of arbitrary axisymmetric rotors supported on rigid bearings. Prior computational treatments of this problem were based on adding element-level gyroscopic terms to the governing equations. Here, we begin with a direct continuum formulation wherein gyroscopic terms need not be added on separately and explicitly: all gyroscopic effects are captured implicitly within the continuum elastodynamics. We present two new methods for obtaining the whirl speed, where we project the dynamic equilibrium equations of the rotor on to a few of its non-spinning vibration mode shapes. The first modal projection method is direct and more accurate, but requires numerical evaluation of more demanding integrals. The second method is iterative and involves a small approximation, but is simpler. Both the methods are based on one new insight: the gyroscopic terms used in other treatments are essentially the result of a prestress in the rotor caused by the non-zero spin rate...

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Research paper thumbnail of Symmetry-breaking transitions in equilibrium shapes of coherent precipitates

Journal of the Mechanics and Physics of Solids, 2000

We present a general approach for determining the equilibrium shape of isolated, coherent, misfit... more We present a general approach for determining the equilibrium shape of isolated, coherent, misfitting particles by minimizing the sum of elastic and interfacial energies using a synthesis of finite element and optimization techniques. The generality derives from the fact that there is no ...

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Research paper thumbnail of An alternative numerical implementation of the Burnett family of acoustic infinite elements

The Journal of the Acoustical Society of America, 2005

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Research paper thumbnail of Topology Design of Structures Subjected to Periodic Loading

Journal of Sound and Vibration, 2002

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Research paper thumbnail of The Explicit Determination of the Logarithm of a Tensor and Its Derivatives

Journal of Elasticity, 2008

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Research paper thumbnail of Shortcomings of discontinuous-pressure finite element methods on a class of transient problems

International Journal for Numerical Methods in Fluids, 2009

ABSTRACT Past studies that have compared LBB stable discontinuous- and continuous-pressure finite... more ABSTRACT Past studies that have compared LBB stable discontinuous- and continuous-pressure finite element formulations on a variety of problems have concluded that both methods yield solutions of comparable accuracy, and that the choice of interpolation is dictated by which of the two is more efficient. In this work, we show that using discontinuous-pressure interpolations can yield inaccurate solutions at large times on a class of transient problems, while the continuous-pressure formulation yields solutions that are in good agreement with the analytical solution. Copyright © 2009 John Wiley & Sons, Ltd.

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Research paper thumbnail of A finite element method for compressible viscous fluid flows

International Journal for Numerical Methods in Fluids, 2010

ABSTRACT This work presents a mixed three-dimensional finite element formulation for analyzing co... more ABSTRACT This work presents a mixed three-dimensional finite element formulation for analyzing compressible viscous flows. The formulation is based on the primitive variables velocity, density, temperature and pressure. The goal of this work is to present a ‘stable’ numerical formulation, and, thus, the interpolation functions for the field variables are chosen so as to satisfy the inf–sup conditions. An exact tangent stiffness matrix is derived for the formulation, which ensures a quadratic rate of convergence. The good performance of the proposed strategy is shown in a number of steady-state and transient problems where compressibility effects are important such as high Mach number flows, natural convection, Riemann problems, etc., and also on problems where the fluid can be treated as almost incompressible. Copyright © 2010 John Wiley & Sons, Ltd.

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Research paper thumbnail of Topology design with optimized, self-adaptive materials

International Journal for Numerical Methods in Engineering, 1994

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Research paper thumbnail of Distributed-parameter optimization and topology design for non-linear thermoelasticity

Computer Methods in Applied Mechanics and Engineering, 1996

... in the presence of thermal loading, the stresses are not proportional to the strains, even in... more ... in the presence of thermal loading, the stresses are not proportional to the strains, even in linearized thermoelasticity. ... This result is analogous to that obtained using the small-strain theory, hence, it would be reasonable to expect that the solid-void compliance optimization ...

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Research paper thumbnail of A Monolithic Finite Element Formulation for Magnetohydrodynamics Involving a Compressible Fluid

Fluids, 2022

This work develops a new monolithic finite-element-based strategy for magnetohydrodynamics (MHD) ... more This work develops a new monolithic finite-element-based strategy for magnetohydrodynamics (MHD) involving a compressible fluid based on a continuous velocity–pressure formulation. The entire formulation is within a nodal finite element framework, and is directly in terms of physical variables. The exact linearization of the variational formulation ensures a quadratic rate of convergence in the vicinity of the solution. Both steady-state and transient formulations are presented for two- and three-dimensional flows. Several benchmark problems are presented, and comparisons are carried out against analytical solutions, experimental data, or against other numerical schemes for MHD. We show a good coarse-mesh accuracy and robustness of the proposed strategy, even at high Hartmann numbers.

Bookmarks Related papers MentionsView impact

Research paper thumbnail of Topology Design of Three-Dimensional Structures Using Hybrid Finite Elements

Solid Mechanics and Its Applications

ABSTRACT Conventional three-dimensional isoparametric elements are susceptible to problems of loc... more ABSTRACT Conventional three-dimensional isoparametric elements are susceptible to problems of locking when used to model plate/shell geometries or when the meshes are distorted etc. Hybrid elements that are based on a two-field variational formulation are immune to most of these problems, and hence can be used to efficiently model both “chunky” three-dimensional and plate/shell type structures. Thus, only one type of element can be used to model “all” types of structures, and also allows us to use a standard dual algorithm for carrying out the topology optimization of the structure. We also address the issue of manufacturability of the designs.

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Research paper thumbnail of A distributed environment for run-time visualization and application steering in computational mechanics

Computing Systems in Engineering, 1992

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Research paper thumbnail of Mixed finite elements for electromagnetic analysis

Computers & Mathematics with Applications, 2014

ABSTRACT The occurrence of spurious solutions is a well-known limitation of the standard nodal fi... more ABSTRACT The occurrence of spurious solutions is a well-known limitation of the standard nodal finite element method when applied to electromagnetic problems. The two commonly used remedies that are used to address this problem are (i) The addition of a penalty term with the penalty factor based on the local dielectric constant, and which reduces to a Helmholtz form on homogeneous domains (regularized formulation); (ii) A formulation based on a vector and a scalar potential. Both these strategies have some shortcomings. The penalty method does not completely get rid of the spurious modes, and both methods are incapable of predicting singular eigenvalues in non-convex domains. Some non-zero spurious eigenvalues are also predicted by these methods on non-convex domains. In this work, we develop mixed finite element formulations which predict the eigenfrequencies (including their multiplicities) accurately, even for nonconvex domains. The main feature of the proposed mixed finite element formulation is that no ad-hoc terms are added to the formulation as in the penalty formulation, and the improvement is achieved purely by an appropriate choice of finite element spaces for the different variables. We show that the formulation works even for inhomogeneous domains where ‘double noding’ is used to enforce the appropriate continuity requirements at an interface. For two-dimensional problems, the shape of the domain can be arbitrary, while for the three-dimensional ones, with our current formulation, only regular domains (which can be nonconvex) can be modeled. Since eigenfrequencies are modeled accurately, these elements also yield accurate results for driven problems.

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Research paper thumbnail of A Note on Boundary Conditions

Foundations and Applications of Mechanics

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Research paper thumbnail of Some Results in n-Dimensional Euclidean Spaces

Foundations and Applications of Mechanics

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Research paper thumbnail of Oblate Spheroidal Coordinate System

Foundations and Applications of Mechanics

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Research paper thumbnail of Nonlinear Elasticity

Foundations and Applications of Mechanics

Bookmarks Related papers MentionsView impact

Research paper thumbnail of Constitutive Equations

Foundations and Applications of Mechanics

Bookmarks Related papers MentionsView impact

Research paper thumbnail of Introduction to Tensors

Foundations and Applications of Mechanics

Bookmarks Related papers MentionsView impact

Research paper thumbnail of A new approach to variable-topology shape design using a constraint on perimeter

Structural Optimization, 1996

Bookmarks Related papers MentionsView impact

Research paper thumbnail of Modal projections for synchronous rotor whirl

Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences, 2008

We consider the synchronous whirl of arbitrary axisymmetric rotors supported on rigid bearings. P... more We consider the synchronous whirl of arbitrary axisymmetric rotors supported on rigid bearings. Prior computational treatments of this problem were based on adding element-level gyroscopic terms to the governing equations. Here, we begin with a direct continuum formulation wherein gyroscopic terms need not be added on separately and explicitly: all gyroscopic effects are captured implicitly within the continuum elastodynamics. We present two new methods for obtaining the whirl speed, where we project the dynamic equilibrium equations of the rotor on to a few of its non-spinning vibration mode shapes. The first modal projection method is direct and more accurate, but requires numerical evaluation of more demanding integrals. The second method is iterative and involves a small approximation, but is simpler. Both the methods are based on one new insight: the gyroscopic terms used in other treatments are essentially the result of a prestress in the rotor caused by the non-zero spin rate...

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Research paper thumbnail of Symmetry-breaking transitions in equilibrium shapes of coherent precipitates

Journal of the Mechanics and Physics of Solids, 2000

We present a general approach for determining the equilibrium shape of isolated, coherent, misfit... more We present a general approach for determining the equilibrium shape of isolated, coherent, misfitting particles by minimizing the sum of elastic and interfacial energies using a synthesis of finite element and optimization techniques. The generality derives from the fact that there is no ...

Bookmarks Related papers MentionsView impact

Research paper thumbnail of An alternative numerical implementation of the Burnett family of acoustic infinite elements

The Journal of the Acoustical Society of America, 2005

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Research paper thumbnail of Topology Design of Structures Subjected to Periodic Loading

Journal of Sound and Vibration, 2002

Bookmarks Related papers MentionsView impact

Research paper thumbnail of The Explicit Determination of the Logarithm of a Tensor and Its Derivatives

Journal of Elasticity, 2008

Bookmarks Related papers MentionsView impact

Research paper thumbnail of Shortcomings of discontinuous-pressure finite element methods on a class of transient problems

International Journal for Numerical Methods in Fluids, 2009

ABSTRACT Past studies that have compared LBB stable discontinuous- and continuous-pressure finite... more ABSTRACT Past studies that have compared LBB stable discontinuous- and continuous-pressure finite element formulations on a variety of problems have concluded that both methods yield solutions of comparable accuracy, and that the choice of interpolation is dictated by which of the two is more efficient. In this work, we show that using discontinuous-pressure interpolations can yield inaccurate solutions at large times on a class of transient problems, while the continuous-pressure formulation yields solutions that are in good agreement with the analytical solution. Copyright © 2009 John Wiley & Sons, Ltd.

Bookmarks Related papers MentionsView impact

Research paper thumbnail of A finite element method for compressible viscous fluid flows

International Journal for Numerical Methods in Fluids, 2010

ABSTRACT This work presents a mixed three-dimensional finite element formulation for analyzing co... more ABSTRACT This work presents a mixed three-dimensional finite element formulation for analyzing compressible viscous flows. The formulation is based on the primitive variables velocity, density, temperature and pressure. The goal of this work is to present a ‘stable’ numerical formulation, and, thus, the interpolation functions for the field variables are chosen so as to satisfy the inf–sup conditions. An exact tangent stiffness matrix is derived for the formulation, which ensures a quadratic rate of convergence. The good performance of the proposed strategy is shown in a number of steady-state and transient problems where compressibility effects are important such as high Mach number flows, natural convection, Riemann problems, etc., and also on problems where the fluid can be treated as almost incompressible. Copyright © 2010 John Wiley & Sons, Ltd.

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Research paper thumbnail of Topology design with optimized, self-adaptive materials

International Journal for Numerical Methods in Engineering, 1994

Bookmarks Related papers MentionsView impact

Research paper thumbnail of Distributed-parameter optimization and topology design for non-linear thermoelasticity

Computer Methods in Applied Mechanics and Engineering, 1996

... in the presence of thermal loading, the stresses are not proportional to the strains, even in... more ... in the presence of thermal loading, the stresses are not proportional to the strains, even in linearized thermoelasticity. ... This result is analogous to that obtained using the small-strain theory, hence, it would be reasonable to expect that the solid-void compliance optimization ...

Bookmarks Related papers MentionsView impact