I am an Emeritus Professor at the Illinois Institute of Technology, Chicago, Illinois. I taught Mechanical and Aerospace Engineering subjects with specialization in Mechanics.
A system of linear equations governing the small deformations of an initially stressed, curved, t... more A system of linear equations governing the small deformations of an initially stressed, curved, twisted composite rod is obtained through the use of the principle of virtual work. Apart from the extensions! and bending deformations, transverse shear as well as warping of the rod cross section are incorporated into the assumed displacement field. The resulting equations are applicable for transversely isotropic rods for a wide range of values of the ratio of the shear modulus to Young's modulus. Special cases of the governing equations are also presented for plane-curved symmetric rods. N this paper, we consider the effect of initial stresses on the small deformations of a curved, twisted rod. The rod is assumed to be transversely isotropic with a heterogeneous cross section. The effect of initial axial stress on the torsional rigidity of straight uniform rods is well-known.1'2 An examination of the formula in Ref. 1 for the effective torsional rigidity reveals that the effect of axial stress is particularly significant whenever the shear modulus of the material is small compared to Young's modulus. Corresponding to this range of values of the shear modulus, the shear deformation of the rod may be significant. In the following treatment, we obtain the effective torsional rigidity for space curved rods in the presence of shear deformation as part of our results. The analysis of the initial stress problem is based on the linearized three-dimensional initial stress problem, and the associated variational principles discussed in Ref. 2. In conjunction with the principle of virtual work, we assume a displacement field incorporating transverse shear deformation and warping of the cross section. In the subsequent considerations, approximations are introduced on the basis of the thinness of the rod to simplify the resulting relations. Inertia forces, associated with the small deformations, are included through the use of D'Alembert's principle. A system of equations for the treatment of symmetric, plane-curved rods is obtained by specializing the general relations. These equations readily uncouple into two sets— one describing the in-plane deformations, the other describing the out-of-plane deformations of the rod. Explicit forms of these relations are also stated for the case of negligible transverse shear deformation. An analysis of superposed small displacements on finite deformations of rods has been previously given by Green et al.3 The constitutive relations obtained in Ref. 3, on the basis of thermodynamically consistent strain energy functions, introduce unnecessary complexity in an approximate treatment of practical rod problems, such as the dynamic stability
International Journal of Vehicle Design, Aug 5, 2014
When a wheel is subjected to repeated thermal loading due to drag braking cracks can develop and ... more When a wheel is subjected to repeated thermal loading due to drag braking cracks can develop and propagate due to fatigue. Wheels of 36, 33 and 28 inch diameter were studied using the finite–element method. The wheels were subjected to drag braking of 30, 40 and 50 hp, each applied for 30 minutes. The fatigue life was computed for an assumed load history using the Miner's linear cumulative damage rule. The temperature distribution in the wheel was obtained by means of the DOT program. The CREEP–PLAST program was used to compute the stress and strain distributions. The stress and strain values increase as the braking horsepower is increased. For the same loading the fatigue life is lower for the smaller wheels as compared to the fatigue life of the larger wheels.
International Journal for Numerical Methods in Engineering, 1978
A numerical scheme based on polynomial approximation is presented for the calculation of upper an... more A numerical scheme based on polynomial approximation is presented for the calculation of upper and lower bounds for the flexibility coefficient of end-loaded orthotrop ic cantilever beam s in a state of plane stress, through use of the principles of minimum potential e n e r g y and of minimum complementary energy. The d e g r e e-o f-f r e e d o m of the twodimensional pol ynomials employed along with the elastic constants and
International Journal of Engineering Science, 1991
Aha&&-The plastic bending of a circular plate due to the normal penetration of a projectile is an... more Aha&&-The plastic bending of a circular plate due to the normal penetration of a projectile is analyzed, including the effect of shear deformation. Dynamic radii of plastic hinges are calculated using a Tresca yield criterion in the generalized stress space formed by the plate bending moments and shear force. The results are compared with experimentally obtained deflection shapes. The experiments were conducted using a gas gun with aluminum plates and steel projectiles.
... a Department of Mechanical Engineering, University of Bahrain, PO Box 32038, Manama, Bahrain.... more ... a Department of Mechanical Engineering, University of Bahrain, PO Box 32038, Manama, Bahrain. ... The governing equilibrium equations for the catenary are (7)(Tx′)′=0, 0 s s o and s o s l, (8)(Ty′)′+ρg=0, 0 s s o and s o s l.The interface conditions at s=s o are obtained as ...
Etude de la configuration d'equilibre plane et de la stabilite sous des perturbations lateral... more Etude de la configuration d'equilibre plane et de la stabilite sous des perturbations laterales et de torsion d'un câble sous-marin de remorquage. Exemple du câble composite de la compagnie Boeing. On utilise la methode de Galerkin pour analyser la stabilite du câble. Les resultats montrent des instabilites sous forme de divergence aux basses vitesses et de flottement aux grandes vitesses avec un remorquage stable aux vitesses intermediaires
Known results on asymptotic two-dimensional equations for circular cylindrical shells, including ... more Known results on asymptotic two-dimensional equations for circular cylindrical shells, including the effects of transverse shear and normal stress deformation, are supplemented by upper-and lower-bound de terminations of influence coefficients, using minimum-potential and complementary energy principles in conjunction with asymptotic-expansion results. The new bound analysis shows that the consequences of the asymptotic two-dimensional theory are in exact agreement, except for terms which are small of higher order, with the corresponding consequences of three-dimensional theory, for some classes of edge conditions. The analysis also shows the nature of the differences between results of two-and three-dimensional theory, as a function of geometrical and elastic parameters, where this difference IS of importance because of the effect of a S1. Venant boundary layer. *A report on work supported by the Office of Naval Research, Washington, D.e.
Zeitschrift für Angewandte Mathematik und Physik, 1974
A previous paper (reference [3]) has formulated a version of the well-known plane stress problem ... more A previous paper (reference [3]) has formulated a version of the well-known plane stress problem of the end-loaded cantilever beam of narrow rectangular cross section in a way which allowed the statement of upper and lower bounds for the deflection of the beam, through use of the principles of minimum potential and complementary energy.
Microcontact models, describing contact of two rough surfaces, are fundamental for the modeling o... more Microcontact models, describing contact of two rough surfaces, are fundamental for the modeling of friction and wear. This paper presents a critical analysis of existing models and discusses their limitations. A new deterministic microcontact model based on conformal/counterformal contact of asperities, as opposed to the combined surface statistics and counterformal asperity contact, is presented. Based on this model, a computer program has been developed. The input data are the digitized 3-D topographies, separately measured from the two contacting surfaces. The program first determines the original mating position and then calculates the surface contact parameters: contact radius, contact pressure, real contact area and the number of elastic, plastic, conformal, and counterformal contacts.
International Journal of Engineering Science, 1986
Abstract The model of a nonuniformly moving screw dislocation in an unbounded elastic medium is e... more Abstract The model of a nonuniformly moving screw dislocation in an unbounded elastic medium is employed to analyze the shear wave-front motion. The elastic motion near the shear wave-front is obtained by inversion to the time domain of the dominant high frequency term. The displacement discontinuity of the dislocation considered is of the form Δu z = U(x)ƒ(t − t R (x)) . Necessary and sufficient conditions for the functional dependence of U ( x ), ƒ(t) and t R ( x ) are established for the existence of a nonsingular velocity field.
This textbook treats solids and fluids in a balanced manner, using thermodynamic restrictions on ... more This textbook treats solids and fluids in a balanced manner, using thermodynamic restrictions on the relation between applied forces and material responses. This unified approach can be appreciated by engineers, physicists, and applied mathematicians with some background in engineering mechanics. It has many examples and about 150 exercises for students to practice. The higher mathematics needed for a complete understanding is provided in the early chapters. This subject is essential for engineers involved in experimental or numerical modeling of material behavior.
A system of linear equations governing the small deformations of an initially stressed, curved, t... more A system of linear equations governing the small deformations of an initially stressed, curved, twisted composite rod is obtained through the use of the principle of virtual work. Apart from the extensions! and bending deformations, transverse shear as well as warping of the rod cross section are incorporated into the assumed displacement field. The resulting equations are applicable for transversely isotropic rods for a wide range of values of the ratio of the shear modulus to Young's modulus. Special cases of the governing equations are also presented for plane-curved symmetric rods. N this paper, we consider the effect of initial stresses on the small deformations of a curved, twisted rod. The rod is assumed to be transversely isotropic with a heterogeneous cross section. The effect of initial axial stress on the torsional rigidity of straight uniform rods is well-known.1'2 An examination of the formula in Ref. 1 for the effective torsional rigidity reveals that the effect of axial stress is particularly significant whenever the shear modulus of the material is small compared to Young's modulus. Corresponding to this range of values of the shear modulus, the shear deformation of the rod may be significant. In the following treatment, we obtain the effective torsional rigidity for space curved rods in the presence of shear deformation as part of our results. The analysis of the initial stress problem is based on the linearized three-dimensional initial stress problem, and the associated variational principles discussed in Ref. 2. In conjunction with the principle of virtual work, we assume a displacement field incorporating transverse shear deformation and warping of the cross section. In the subsequent considerations, approximations are introduced on the basis of the thinness of the rod to simplify the resulting relations. Inertia forces, associated with the small deformations, are included through the use of D'Alembert's principle. A system of equations for the treatment of symmetric, plane-curved rods is obtained by specializing the general relations. These equations readily uncouple into two sets— one describing the in-plane deformations, the other describing the out-of-plane deformations of the rod. Explicit forms of these relations are also stated for the case of negligible transverse shear deformation. An analysis of superposed small displacements on finite deformations of rods has been previously given by Green et al.3 The constitutive relations obtained in Ref. 3, on the basis of thermodynamically consistent strain energy functions, introduce unnecessary complexity in an approximate treatment of practical rod problems, such as the dynamic stability
International Journal of Vehicle Design, Aug 5, 2014
When a wheel is subjected to repeated thermal loading due to drag braking cracks can develop and ... more When a wheel is subjected to repeated thermal loading due to drag braking cracks can develop and propagate due to fatigue. Wheels of 36, 33 and 28 inch diameter were studied using the finite–element method. The wheels were subjected to drag braking of 30, 40 and 50 hp, each applied for 30 minutes. The fatigue life was computed for an assumed load history using the Miner's linear cumulative damage rule. The temperature distribution in the wheel was obtained by means of the DOT program. The CREEP–PLAST program was used to compute the stress and strain distributions. The stress and strain values increase as the braking horsepower is increased. For the same loading the fatigue life is lower for the smaller wheels as compared to the fatigue life of the larger wheels.
International Journal for Numerical Methods in Engineering, 1978
A numerical scheme based on polynomial approximation is presented for the calculation of upper an... more A numerical scheme based on polynomial approximation is presented for the calculation of upper and lower bounds for the flexibility coefficient of end-loaded orthotrop ic cantilever beam s in a state of plane stress, through use of the principles of minimum potential e n e r g y and of minimum complementary energy. The d e g r e e-o f-f r e e d o m of the twodimensional pol ynomials employed along with the elastic constants and
International Journal of Engineering Science, 1991
Aha&&-The plastic bending of a circular plate due to the normal penetration of a projectile is an... more Aha&&-The plastic bending of a circular plate due to the normal penetration of a projectile is analyzed, including the effect of shear deformation. Dynamic radii of plastic hinges are calculated using a Tresca yield criterion in the generalized stress space formed by the plate bending moments and shear force. The results are compared with experimentally obtained deflection shapes. The experiments were conducted using a gas gun with aluminum plates and steel projectiles.
... a Department of Mechanical Engineering, University of Bahrain, PO Box 32038, Manama, Bahrain.... more ... a Department of Mechanical Engineering, University of Bahrain, PO Box 32038, Manama, Bahrain. ... The governing equilibrium equations for the catenary are (7)(Tx′)′=0, 0 s s o and s o s l, (8)(Ty′)′+ρg=0, 0 s s o and s o s l.The interface conditions at s=s o are obtained as ...
Etude de la configuration d'equilibre plane et de la stabilite sous des perturbations lateral... more Etude de la configuration d'equilibre plane et de la stabilite sous des perturbations laterales et de torsion d'un câble sous-marin de remorquage. Exemple du câble composite de la compagnie Boeing. On utilise la methode de Galerkin pour analyser la stabilite du câble. Les resultats montrent des instabilites sous forme de divergence aux basses vitesses et de flottement aux grandes vitesses avec un remorquage stable aux vitesses intermediaires
Known results on asymptotic two-dimensional equations for circular cylindrical shells, including ... more Known results on asymptotic two-dimensional equations for circular cylindrical shells, including the effects of transverse shear and normal stress deformation, are supplemented by upper-and lower-bound de terminations of influence coefficients, using minimum-potential and complementary energy principles in conjunction with asymptotic-expansion results. The new bound analysis shows that the consequences of the asymptotic two-dimensional theory are in exact agreement, except for terms which are small of higher order, with the corresponding consequences of three-dimensional theory, for some classes of edge conditions. The analysis also shows the nature of the differences between results of two-and three-dimensional theory, as a function of geometrical and elastic parameters, where this difference IS of importance because of the effect of a S1. Venant boundary layer. *A report on work supported by the Office of Naval Research, Washington, D.e.
Zeitschrift für Angewandte Mathematik und Physik, 1974
A previous paper (reference [3]) has formulated a version of the well-known plane stress problem ... more A previous paper (reference [3]) has formulated a version of the well-known plane stress problem of the end-loaded cantilever beam of narrow rectangular cross section in a way which allowed the statement of upper and lower bounds for the deflection of the beam, through use of the principles of minimum potential and complementary energy.
Microcontact models, describing contact of two rough surfaces, are fundamental for the modeling o... more Microcontact models, describing contact of two rough surfaces, are fundamental for the modeling of friction and wear. This paper presents a critical analysis of existing models and discusses their limitations. A new deterministic microcontact model based on conformal/counterformal contact of asperities, as opposed to the combined surface statistics and counterformal asperity contact, is presented. Based on this model, a computer program has been developed. The input data are the digitized 3-D topographies, separately measured from the two contacting surfaces. The program first determines the original mating position and then calculates the surface contact parameters: contact radius, contact pressure, real contact area and the number of elastic, plastic, conformal, and counterformal contacts.
International Journal of Engineering Science, 1986
Abstract The model of a nonuniformly moving screw dislocation in an unbounded elastic medium is e... more Abstract The model of a nonuniformly moving screw dislocation in an unbounded elastic medium is employed to analyze the shear wave-front motion. The elastic motion near the shear wave-front is obtained by inversion to the time domain of the dominant high frequency term. The displacement discontinuity of the dislocation considered is of the form Δu z = U(x)ƒ(t − t R (x)) . Necessary and sufficient conditions for the functional dependence of U ( x ), ƒ(t) and t R ( x ) are established for the existence of a nonsingular velocity field.
This textbook treats solids and fluids in a balanced manner, using thermodynamic restrictions on ... more This textbook treats solids and fluids in a balanced manner, using thermodynamic restrictions on the relation between applied forces and material responses. This unified approach can be appreciated by engineers, physicists, and applied mathematicians with some background in engineering mechanics. It has many examples and about 150 exercises for students to practice. The higher mathematics needed for a complete understanding is provided in the early chapters. This subject is essential for engineers involved in experimental or numerical modeling of material behavior.
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Papers by Sudhakar Nair