TEACHING (ARCHIVES)
TEACHING (SPRING 2022)
CE 284 : PLATES, SHELLS, AND GEOMETRIC ELASTICITY (3:0)
Timing: Tu Thu 11:30am Venue: Online / MS TEAMS
Description
CE 284 is a graduate-level elective which aims to provide a broad and modernized introduction to the theory of plates and shells. All requisite mathematical tools will be covered in-course.
A background graduate-level solid mechanics course (CE 204 / ME 242 or equivalent) is recommended. Please email me if you have any questions.
The course will be taught online via MS-TEAMS this semester.
To apply to join the class, please use
this link.
Students will also be able to access the course channel via the
Institute academic intranet page (login required)
COURSE NEWS AND UPDATES
ANNOUNCEMENT:The TA for the class is B. Karthikeyan.
ANNOUNCEMENT:The first class of CE 284 will be held on Tuesday, 6th January at 11:30 am on MS-TEAMS.
Brief Outline
Review of elasticity and variational principles; classical plate theories; shear plates; elements of large deflection of thin plates; applications of plate theories; differential geometry of surfaces in R^3; curvature; shell theories; engineering applications. Other topics as time permits
TEACHING (FALL 2021)
CE 204 : SOLID MECHANICS (3:0)
Timing: MWF 2:00 pm Venue: ONLINE / MS TEAMS
Description
CE 204 is a graduate-level core course in solid mechanics and is mandatory for all incoming CiE MTech students.
The course has a mix of topics from traditional Continuum Mechanics, Theory of Elasticity, and Advanced Structural Analysis.
COURSE NEWS AND UPDATES
ANNOUNCEMENT:The first class of CE 204 (Solid Mechanics) will be held online on Wednesday, 4th August at 2:00 pm.
Outline
Introduction to tensor algebra and calculus, indicial notation, matrices of tensor components, change of basis formulae, eigenvalues, Divergence theorem. Elementary measures of strain. Lagrangian and Eulerian description of deformation. Deformation gradient, Polar decomposition theorem, Cauchy-Green and Lagrangian strain tensors. Deformation of lines, areas and volumes. Infinitesimal strains. Infinitesimal strain-displacement relations in cylindrical and spherical coordinates. Compatibility.
Tractions, body forces, stress at a point, Cauchy's theorem. Piola-Kirchhoff stress tensors. Momentum balance. Symmetry of the Cauchy stress tensor. St. Venant's Principle. Virtual Work. Green's solids, elastic strain energy, generalized Hooke's Law, material symmetry, isotropic linear elasticity in Cartesian, cylindrical and spherical coordinates, elastic moduli, plane stress, plane strain.
Navier's formulation. Airy stress functions. Selected problems in elasticity. Kirchhoff's uniqueness theorem, Betti-Maxwell reciprocal theorem, Principle of stationary potential energy. Torsion in circular and non-circular shafts and thin-walled tubes, warping.
TEACHING (SPRING 2021)
CE 297 : PROBLEMS IN THE MATHEMATICAL THEORY OF ELASTICITY (3:0)
Timing: Tu Thu 11:30am Venue: Online / MS TEAMS
Description
CE 297 is a graduate-level elective course that provides an in-depth look at a variety of important problems in the theory of elasticity, and introduces powerful tools from complex analysis and potential theory for their solution. This course is intended for students from civil engineering, mechanical engineering and aerospace engineering who have done at least one graduate-level solid mechanics course (CE 204 / ME 242 or equivalent). Please meet me if you do not have any prior coursework.
The course will be taught online via MS-TEAMS this semester.
COURSE NEWS AND UPDATES
ANNOUNCEMENT:The first class of CE 297 will be held on Tuesday, 23th February at 11:30 am.
Brief Outline
Introduction to functions of one complex variable and boundary value problems; Kolosov-Muskhelishvili formulation for planar elasticity; Solution of selected problems in the theory of elasticity for circular disks, plates with circular and elliptical holes, half-planes, slit infinite planes. Other topics as time permits.
TEACHING (FALL 2020)
CE 204 : SOLID MECHANICS (3:0)
Timing: MWF 2:00 pm Venue: ONLINE / MS TEAMS
Description
CE 204 is a graduate-level core course in solid mechanics and is mandatory for all incoming CiE MTech students.
The course has a mix of topics from traditional Continuum Mechanics, Theory of Elasticity, and Advanced Structural Analysis.
COURSE NEWS AND UPDATES
Outline
Introduction to tensor algebra and calculus, indicial notation, matrices of tensor components, change of basis formulae, eigenvalues, Divergence theorem. Elementary measures of strain. Lagrangian and Eulerian description of deformation. Deformation gradient, Polar decomposition theorem, Cauchy-Green and Lagrangian strain tensors. Deformation of lines, areas and volumes. Infinitesimal strains. Infinitesimal strain-displacement relations in cylindrical and spherical coordinates. Compatibility.
Tractions, body forces, stress at a point, Cauchy's theorem. Piola-Kirchhoff stress tensors. Momentum balance. Symmetry of the Cauchy stress tensor. St. Venant's Principle. Virtual Work. Green's solids, elastic strain energy, generalized Hooke's Law, material symmetry, isotropic linear elasticity in Cartesian, cylindrical and spherical coordinates, elastic moduli, plane stress, plane strain.
Navier's formulation. Airy stress functions. Selected problems in elasticity. Kirchhoff's uniqueness theorem, Betti-Maxwell reciprocal theorem, Principle of stationary potential energy. Torsion in circular and non-circular shafts and thin-walled tubes, warping. Pure bending of thin rectangular and circular plates, small deflection problems in laterally loaded thin rectangular and circular plates.
Outline of Mindlin plate theory.
References
Fung, Y. C. and Pin Tong, Classical and Computational Solid Mechanics, World Scientific, 2001
Boresi, A.P., Chong K., and Lee J., Elasticity in Engineering Mechanics, Wiley, 2010
Theoretical Elasticity, A.E. Green and W. Zerna, 1968, Dover Publications
Malvern L., Introduction to the Mechanics of a Continuous Medium, Prentice Hall, 1969
TEACHING (SPRING 2020)
CE 297 : PROBLEMS IN THE MATHEMATICAL THEORY OF ELASTICITY (3:0)
Timing: Tu Thu 11:30 am-1:00 pm Venue: STLH Structures Lab Building
Description
CE 297 is a graduate-level elective course that provides an in-depth look at a variety of important problems in the theory of elasticity, and introduce powerful tools from complex analysis and potential theory for their solution. This course is intended for students from civil engineering, mechanical engineering, aerospace engineering, and earth sciences who have done at least one graduate-level solid mechanics course (CE 204 / ME 242 or equivalent). Please meet me if you do not have any prior coursework.
COURSE NEWS AND UPDATES
Please email me if you want a copy of the typed notes of CE 297 or details of the topics covered.
Brief Outline
Introduction to functions of a complex variable and boundary value problems; Kolosov-Muskhelishvili formulation for planar elasticity; Solution of selected problems in the theory of elasticity for circular disks, plates with circular and elliptical holes and half-planes.
TEACHING (FALL 2019)
CE 204 : SOLID MECHANICS (3:0)
Timing: MWF 2:00 pm Venue: Central Lecture Hall CL7
Description
CE 204 is a graduate-level core course in solid mechanics and is mandatory for all incoming CiE MTech students.
The course has a blend of topics from traditional Continuum Mechanics, Theory of Elasticity, and Advanced Structural Analysis.
COURSE NEWS AND UPDATES
ANNOUNCEMENT:The first class of CE 204 (Solid Mechanics) will be held on Monday, 7th August at 2:00 pm in Room CL7 of the Central Lecture Hall Complex.
Outline
Introduction to tensor algebra and calculus, indicial notation, matrices of tensor components, change of basis formulae, eigenvalues, Divergence theorem. Elementary measures of strain. Lagrangian and Eulerian description of deformation. Deformation gradient, Polar decomposition theorem, Cauchy-Green and Lagrangian strain tensors. Deformation of lines, areas and volumes. Infinitesimal strains. Infinitesimal strain-displacement relations in cylindrical and spherical coordinates. Compatibility.
Tractions, body forces, stress at a point, Cauchy's theorem. Piola-Kirchhoff stress tensors. Momentum balance. Symmetry of the Cauchy stress tensor. St. Venant's Principle. Virtual Work. Green's solids, elastic strain energy, generalized Hooke's Law, material symmetry, isotropic linear elasticity in Cartesian, cylindrical and spherical coordinates, elastic moduli, plane stress, plane strain.
Navier's formulation. Airy stress functions. Selected problems in elasticity. Kirchhoff's uniqueness theorem, Betti-Maxwell reciprocal theorem, Principle of stationary potential energy. Torsion in circular and non-circular shafts and thin-walled tubes, warping. Pure bending of thin rectangular and circular plates, small deflection problems in laterally loaded thin rectangular and circular plates.
Outline of Mindlin plate theory.
References
Fung, Y. C. and Pin Tong, Classical and Computational Solid Mechanics, World Scientific, 2001
Boresi, A.P., Chong K., and Lee J., Elasticity in Engineering Mechanics, Wiley, 2010
Theoretical Elasticity, A.E. Green and W. Zerna, 1968, Dover Publications
Malvern L., Introduction to the Mechanics of a Continuous Medium, Prentice Hall, 1969
TEACHING (FALL 2018)
CE 204 : SOLID MECHANICS (3:0)
M W F 2:00pm Venue: CL7, Central Lecture Hall Complex
Description
CE 204 is a graduate-level core course in solid mechanics and is mandatory for all incoming CiE MTech students.
The course has a blend of topics from traditional Continuum Mechanics, Theory of Elasticity, and Advanced Structural Analysis.
COURSE NEWS AND UPDATES
ANNOUNCEMENT: The first class of CE 204 (Solid Mechanics) will be held on Monday, 6th August at 2:00 pm in Room CL7 of the Central Lecture Hall Complex.
TEACHING (SPRING 2017)
CE 228 : INTRODUCTION TO THE THEORY OF PLASTICITY (3:0)
T Th 2:00pm Venue: STLH, Structures Lab, Civil Engineering
Description
CE 228 is a graduate-level plasticity theory course designed for a broad audience of engineering students. While there are no formal prerequisites, a background grad-level course in solid mechanics (or an equivalent) is desirable.
COURSE NEWS AND UPDATES
ANNOUNCEMENT: The first class of CE-228 will be held on Tuesday, 10th January at 2:00 pm in the STLH lecture room.
Outline
1D plasticity and visco-plasticity; physical basis of plasticity; uniaxial tensile test & Bauschinger effect; structure of phenomenological plasticity theories; internal variables; yield criteria (Tresca, von Mises, Mohr-Coulomb, DruckerPrager); geometry of yield surfaces; LevyMises equations; flow rules; plastic/ viscoplastic potentials; consistency condition; isotropic and kinematic hardening; Drucker's postulate; Principle of maximum plastic dissipation; associativity; convexity; normality; uniqueness; selected elastic-plastic boundary value problems (tension and torsion of tubes and rods, pressurized thin and thick spherical shells); collapse; advanced hardening models; introduction to computational plasticity; integration of plasticity models; return mapping; principle of virtual work; Finite elements for plasticity
References
Plasticity Theory - J. Lubliner
Plasticity for Engineers - C. R. Calladine
Theory of Plasticity - J. Chakrabarty
TEACHING (FALL 2016)
CE 204 : SOLID MECHANICS (3:0)
M W F 2:00pm Venue: CL9, Central Lecture Hall Complex
Description
CE 204 is a graduate-level core course in solid mechanics and is mandatory for all incoming CiE MTech students.
The course has a blend of topics from traditional Continuum Mechanics, Theory of Elasticity and Advanced Structural Analysis.
Outline
Introduction to tensor algebra and calculus, indicial notation, matrices of tensor components, change of basis formulae, eigenvalues, Divergence theorem. Elementary measures of strain. Lagrangian and Eulerian description of deformation. Deformation gradient, Polar decomposition theorem, Cauchy-Green and Lagrangian strain tensors. Deformation of lines, areas and volumes. Infinitesimal strains. Infinitesimal strain-displacement relations in cylindrical and spherical coordinates. Compatibility.
Tractions, body forces, stress at a point, Cauchy's theorem. Piola-Kirchhoff stress tensors. Momentum balance. Symmetry of the Cauchy stress tensor. St. Venant's Principle. Virtual Work. Green's solids, elastic strain energy, generalized Hooke's Law, material symmetry, isotropic linear elasticity in Cartesian, cylindrical and spherical coordinates, elastic moduli, plane stress, plane strain.
Navier's formulation. Airy stress functions. Selected problems in elasticity. Kirchhoff's uniqueness theorem, Betti-Maxwell reciprocal theorem, Principle of stationary potential energy. Torsion in circular and non-circular shafts and thin-walled tubes, warping. Pure bending of thin rectangular and circular plates, small deflection problems in laterally loaded thin rectangular and circular plates.
Outline of Mindlin plate theory.
References
Fung, Y. C. and Pin Tong, Classical and Computational Solid Mechanics, World Scientific, 2001
Boresi, A.P., Chong K., and Lee J., Elasticity in Engineering Mechanics, Wiley, 2010
Theoretical Elasticity, A.E. Green and W. Zerna, 1968, Dover Publications
Malvern L., Introduction to the Mechanics of a Continuous Medium, Prentice Hall, 1969
SPRING 2016
CE 228N / 241 : INTRODUCTION TO THE THEORY OF PLASTICITY (3:0)
T Th 11:30-13:00 Venue: STLH, CiE
COURSE UPDATES
The course assignment is due on Friday, 15th April by 5:30 pm. Please make sure your reports include a printout of your MATLAB source code.
Put the assignment report in my mailbox if I am not in.
Description
CE 228N / 241 is an introductory, graduate-level plasticity theory course designed for a broad audience of engineering students.
I co-teach this course with Tejas Murthy.
1D plasticity and visco-plasticity; physical basis of plasticity; uniaxial tensile test & Bauschinger effect; structure of phenomenological plasticity theories; internal variables; yield criteria (Tresca, von Mises, Mohr-Coulomb, DruckerPrager); geometry of yield surfaces; LevyMises equations; flow rules; plastic/ viscoplastic potentials; consistency condition; isotropic and kinematic hardening; Drucker's postulate; Principle of maximum plastic dissipation; associativity; convexity; normality; uniqueness; selected elastic-plastic boundary value problems (tension and torsion of tubes and rods, pressurized thin and thick spherical shells); collapse; advanced hardening models; introduction to computational plasticity; integration of plasticity models; return mapping; principle of virtual work; Finite elements for plasticity
References
Plasticity Theory - J. Lubliner
Plasticity for Engineers - C. R. Calladine
Theory of Plasticity - J. Chakrabarty
FALL 2015
CE 204N / CE 214 : SOLID MECHANICS (3:0)
M W F 10:00am Venue: CL5 Lecture Hall Complex
Description
CE 204N / 214 is a graduate-level core course and is mandatory for all incoming CiE ME students.
The course has a blend of topics from traditional Continuum Mechanics, Theory of Elasticity and Structural Analysis.
COURSE NEWS AND UPDATES
Outline
Introduction to tensor algebra and calculus, indicial notation, matrices of tensor components, change of basis formulae, eigenvalues, Divergence theorem. Elementary measures of strain. Lagrangian and Eulerian description of deformation. Deformation gradient, Polar decomposition theorem, Cauchy-Green and Lagrangian strain tensors. Deformation of lines, areas and volumes. Infinitesimal strains. Infinitesimal strain-displacement relations in cylindrical and spherical coordinates. Compatibility.
Tractions, body forces, stress at a point, Cauchy's theorem. Piola-Kirchhoff stress tensors. Momentum balance. Symmetry of the Cauchy stress tensor. St. Venant's Principle. Virtual Work. Green's solids, elastic strain energy, generalized Hooke's Law, material symmetry, isotropic linear elasticity in Cartesian, cylindrical and spherical coordinates, elastic moduli, plane stress, plane strain.
Navier's formulation. Airy stress functions. Selected problems in elasticity. Kirchhoff's uniqueness theorem, Betti-Maxwell reciprocal theorem, Principle of stationary potential energy. Torsion in circular and non-circular shafts and thin-walled tubes, warping. Pure bending of thin rectangular and circular plates, small deflection problems in laterally loaded thin rectangular and circular plates.
Outline of Mindlin plate theory. Introduction to yield and plasticity.
References
Fung, Y. C. and Pin Tong, Classical and Computational Solid Mechanics, World Scientific, 2001
Boresi, A.P., Chong K., and Lee J., Elasticity in Engineering Mechanics, Wiley, 2010*
Theoretical Elasticity, A.E. Green and W. Zerna, 1968, Dover Publications
*This is a newer edition of the 1974 text by Lynn and Boresi
TEACHING (SPRING 2015)
CE 241 : INTRODUCTION TO THE THEORY OF PLASTICITY (3:0)
T Th 08:00-09:30 Venue: GTLH, CiE
I taught this course with Tejas Murthy.
COURSE UPDATES
The first class of CE-241 will be held on 6th January, Tuesday.
Description
CE 241 is an introductory plasticity theory course designed for a broad audience of engineering students.
It covers classical plasticity and viscoplasticity, introductory computational plasticity and also includes a refresher on linear elasticity.
Topics covered include:
1D plasticity and viscoplasticity; physical basis of plasticity; uniaxial tensile test & Bauschinger effect; phenomenological basis of assumptions in plasticity; Levy-Mises equations; yield criteria (Tresca, von Mises, Mohr-Coulomb, Drucker-Prager); geometry of yield surfaces; flow rules and hardening ; plastic / viscoplastic potentials; Drucker's postulate; convexity; normality; Illyushin's principle; shakedown; problems in rigid-perfectly plastic solids; slipline fields; introduction to upper and lower bounds; selected rigid-perfectly plastic and elastic-plastic boundary value problems; advanced hardening models; introduction to computational plasticity; radial return and other integration algorithms; other topics as time permits.
References
Plasticity Theory - J. Lubliner
Plasticity for Engineers - C. R. Calladine
Theory of Plasticity - J. Chakrabarty
FALL 2014
CE 214 : SOLID MECHANICS (3:0)
M W F 11:00-12:00 Venue: STLH, CiE
Description
CE 214 is a graduate-level core course and is mandatory for CiE students with Structural Engineering as their major.
The course has a blend of topics from traditional Continuum Mechanics, Theory of Elasticity and Structural Analysis.
Outline
Introduction to tensor algebra and calculus, indicial notation, matrices of tensor components, change of basis formulae, eigenvalues, Divergence theorem. Elementary measures of strain. Lagrangian and Eulerian description of deformation. Deformation gradient, Polar decomposition theorem, Cauchy-Green and Lagrangian strain tensors. Deformation of lines, areas and volumes. Infinitesimal strains. Infinitesimal strain-displacement relations in cylindrical and spherical coordinates. Compatibility.
Tractions, body forces, stress at a point, Cauchy's theorem. Piola-Kirchhoff stress tensors. Momentum balance. Symmetry of the Cauchy stress tensor. St. Venant's Principle. Virtual Work. Green's solids, elastic strain energy, generalized Hooke's Law, material symmetry, isotropic linear elasticity in Cartesian, cylindrical and spherical coordinates, elastic moduli, plane stress, plane strain.
Navier's formulation. Airy stress functions. Selected problems in elasticity. Kirchhoff's uniqueness theorem, Betti-Maxwell reciprocal theorem, Principle of stationary potential energy. Torsion in circular and non-circular shafts and thin-walled tubes, warping. Pure bending of thin rectangular and circular plates, small deflection problems in laterally loaded thin rectangular and circular plates.
Outline of Mindlin plate theory. Introduction to yield and plasticity.
References
Fung, Y. C. and Pin Tong, Classical and Computational Solid Mechanics, World Scientific, 2001
Boresi, A.P., Chong K., and Lee J., Elasticity in Engineering Mechanics, Wiley, 2010*
Theoretical Elasticity, A.E. Green and W. Zerna, 1968, Dover Publications
*This is a newer edition of the 1974 text by Lynn and Boresi
SPRING 2014
CE 241 : INTRODUCTION TO THE THEORY OF PLASTICITY (3:0)
I co-taught this course with Tejas Murthy.
Outline
CE 241 is an introductory plasticity theory course designed for a broad audience of engineering students. It
covers classical plasticity and viscoplasticity, and includes a refresher on deformation, linear elasticity
and tensors. Topics covered include:
1D plasticity and viscoplasticity; physical basis of plasticity; uniaxial tensile test & Bauschinger effect; phenomenological basis of assumptions in plasticity; Levy-Mises equations; yield criteria (Tresca, von Mises, Mohr-Coulomb, Drucker-Prager); geometry of yield surfaces; flow rules and hardening ; plastic / viscoplastic potentials; Drucker's postulate; convexity; normality; Illyushin's principle; shakedown; problems in rigid-perfectly plastic solids; slipline fields; introduction to upper and lower bounds; selected rigid-perfectly plastic and elastic-plastic boundary value problems; advanced hardening models; introduction to computational plasticity; radial return and other integration algorithms; other topics as time permits.
References
Plasticity Theory - J. Lubliner
Plasticity for Engineers - C. R. Calladine
Theory of Plasticity - J. Chakrabarty