Showing papers by "J. N. Reddy published in 1976"

An introduction to the mathematical theory of finite elements

Abstract: On Engineering By J T Oden J N Reddy ONLINE SHOPPING FOR NUMBER INTRODUCTION AN INTRODUCTION. MATHEMATICAL LEARNING THEORY R C ATKINSON. AN INTRODUCTION TO THE MATHEMATICAL THEORY OF INVERSE. AN INTRODUCTION TO THE MATHEMATICAL THEORY OF FINITE. AN INTRODUCTION TO THE MATHEMATICAL THEORY OF WAVES. AN INTRODUCTION TO THE MATHEMATICAL THEORY OF INVERSE. AN INTRODUCTION TO THE MATHEMATICAL THEORY OF THE NAVIER. AN INTRODUCTION TO THE MATHEMATICAL THEORY OF VIBRATIONS. AN INTRODUCTION TO THE MATHEMATICAL THEORY OF INVERSE. INTRODUCTION MATHEMATICAL THEORY FINITE ELEMENTS ABEBOOKS. AN INTRODUCTION TO THE MATHEMATICAL THEORY OF WAVES. AN INTRODUCTION TO THE

Variational Methods in Theoretical Mechanics

Abstract: 1. Introduction.- 1.1 The Role of Variational Theory in Mechanics.- 1.2 Some Historical Comments.- 1.3 Plan of Study.- 2. Mathematical Foundations of Classical Variational Theory.- 2.1 Introduction.- 2.2 Nonlinear Operators.- 2.3 Differentiation of Operators.- 2.4 Mean Value Theorems.- 2.5 Taylor Formulas.- 2.6 Gradients of Functionals.- 2.7 Minimization of Functionals.- 2.8 Convex Functionals.- 2.9 Potential Operators and the Inverse Problem.- 2.10 Sobolev Spaces.- 3. Mechanics of Continua- A Brief Review.- 3.1 Introduction.- 3.2 Kinematics.- 3.3 Stress and the Mechanical Laws of Balance.- The Principle of Conservation of Mass.- The Principle of Balance of Linear Momentum.- The Principle of Balance of Angular Momentum.- 3.4 Thermodynamic Principles.- The Principle of Conservation of Energy.- The Clausius-Duhem Inequality.- 3.5 Constitutive Theory.- Rules of Constitutive Theory.- Special Forms of Constitutive Equations.- 3.6 Jump Conditions for Discontinuous Fields.- 4. Complementary and Dual Variational Principles in Mechanics.- 4.1 Introduction.- 4.2 Boundary Conditions and Green's Formulas.- 4.3 Examples from Mechanics and Physics.- 4.4 The Fourteen Fundamental Complementary-Dual Principles.- 4.5 Some Complementary-Dual Variational Principles of Mechanics and Physics.- 4.6 Legendre Transformations.- 4.7 Generalized Hamiltonian Theory.- 4.8 Upper and Lower Bounds and Existence Theory.- 4.9 Lagrange Multipliers.- 5. Variational Principles in Continuum Mechanics.- 5.1 Introduction.- 5.2 Some Preliminary Properties and Lemmas.- 5.3 General Variational Principles for Linear Theory of Dynamic Viscoelasticity.- 5.4 Gurtin's Variational Principles for the Linear Theory of Dynamic Viscoelasticity.- 5.5 Variational Principles for Linear Coupled Dynamic Thermoviscoelasticity.- Linear (Coupled) Thermoelasticity.- 5.6 Variational Principles in Linear Elastodynamics.- 5.7 Variational Principles for Linear Piezoelectric Elastodynamic Problems.- 5.8 Variational Principles for Hyperelastic Materials.- Finite Elasticity.- Quasi-Static Problems.- 5.9 Variational Principles in the Flow Theory of Plasticity.- 5.10 Variational Principles for a Large Displacement Theory of Elastoplasticity.- 5.11 Variational Principles in Heat Conduction.- 5.12 Biot's Quasi-Variational Principle in Heat Transfer.- 5.13 Some Variational Principles in Fluid Mechanics and Magnetohydrodynamics.- Non-Newtonian Fluids.- Perfect Fluids.- An Alternate Principle for Invicid Flow.- Magnetohydrodynamics.- 5.14 Variational Principles for Discontinuous Fields.- Hybrid Variational Principles.- 6. Variational Boundary-Value Problems, Monotone Operators, and Variational Inequalities.- 6.1 Direct Variational Methods.- 6.2 Linear Elliptic Variational Boundary-Value Problems.- Regularity.- 6.3 The Lax-Milgram-Babuska Theorem.- 6.4 Existence Theory in Linear Incompressible Elasticity.- 6.5 Monotone Operators.- 6.6 Variational Inequalities.- 6.7 Applications in Mechanics.- 7. Variational Methods of Approximation.- 7.1 Introduction.- 7.2 Several Variational Methods of Approximation.- Galerkin's Method.- The Rayleigh-Ritz Method.- Semidiscrete Galerkin Methods.- Methods of Weighted Residuals.- Least Square Approximations.- Collocation Methods.- Functional Imbeddings.- 7.3 Finite-Element Approximations.- 7.4 Finite-Element Interpolation Theory.- 7.5 Existence and Uniqueness of Galerkin Approximations.- 7.6 Convergence and Accuracy of Finite-Element Galerkin Approximations.- References.

Multiple function pressure sensor

Abstract: Disclosed herein is a multiple function pressure sensor for use in combination with an electronic fuel injection system for an internal combustion engine. The preferred embodiment has two pressure sensitive elements in a single housing which generate signals indicative of the absolute pressure in the engine's intake manifold and the absolute value of the ambient or atmospheric pressure. Included electronic circuitry subtracts the value of the engine's manifold pressure from the value of the atmospheric pressure and generates a third pressure signal indicative of the difference between the manifold pressure and atmospheric pressure. These three pressure signals are utilized in the electronic fuel injection system for computing the fuel requirements of the engine under various operating conditions.

On Mixed Finite Element Approximations

Abstract: A theory of mixed finite element approximations of a class of linear self-adjoint boundary value problems is developed which involves splitting a problem of the type $T^ * Tu = f$ into a pair of canonical equations, $Tu = {\bf v}$, $T^ * v = f$. Consistency and stability of Galerkin/finite element approximations of the pair is described, convergence criteria are established, and error estimates are derived For a number of important cases.

On Complementary Variational Principles for the Linear Theory of Plates

Abstract: A set of complementary variational principles is developed for the linear theory of plates which yields as special cases the minimum potential energy, minimum complementary energy, and Hellinger-Reissner and Hu-Washizu-type variational principles for the linear theory of plates. The governing (biharmonic) equation is decomposed into a set of lower order (differential) equations involving the deflection, slopes, curvatures, moments, and shear forces. A general variational principle is constructed using Vainberg's theory for the set so that all the dependent variables can be varied independently. When one or more equations of the set are satisfied identically, the lower bounds on the functionals are also established. The theory developed herein is generalized to operator equations of the form Lu = fwith the assumption that the linear operator L is decomposable into lower order linear differential operators. It is believed that the variational principles developed herein can be used for the approxim...