Christian Constanda

Integral methods in science and engineering

Mathematical Modeling of N-Body Quantum Scattering Processes Microhydrodynamics of Sharp Corners and Edges Acoustic Scattering by Irregular Obstacles On Generalized Inverse Steklov Problems A Hybrid Root Finder Volterra Type Integral Geometry Problems Inversionof the X-Ray Transform and the Radon Transform with Incomplete Data Reconstructing a Function by means of Integrals over a Family of Conical Surfaces On the use of Wavelet Expansions and the Conjugate Gradient Method for Solving First Kind Integral Equations Optimal Algorithms for the Calculation of Singular Integrals An Order One Approximate Method of Solution of Differential and Integral Equations A Multigrid Method for Solving Reaction-Diffusion Systems Time-Dependent Bending of Plates with Transverse Shear Deformation Polarization Gradient in Piezoelectric Micropolar Elasticity Thermoelastic Stress Separation via Poisson Equation Solution by means of the Boundary Element Method On Neutral Functional Differential Equations with Causal Operations A Semi-Analytic Method for the Study of Acoustic Pulse Propagation in Inhomogeneous Elastic 1-D Media Efficient Finite Elements for the Numerical Approximation of Cylindrical Shells Error Estimates for Computing Fixed Densities of Markov Integral Operators A Modified Monte Carlo Approach to the Approximation of Invariant Measures Acceleration Waves in von Karman Plate Theory Dynamics and Resonance of a Nonlinear Mechanical Oscillator Subjected to Parametric and External Excitation On the Vibration of Helical Springs A Two-Dimensional Numerical Model of Chemotaxis Asymptotic Analysis of Fracture Theory for Layered Composites in Compression (The Plane Problem) Existence and Regularity of Weak Solutions to the Displacement Boundary Value Problem of Nonlinear Elastostatics On Convergence and Uniqueness of Microscale Heat Transfer Equation On Numerical Approximations of a Frictionless Contact Problem for Elastic-Viscoplastic Materials A Panel Clustering Method for 3-D Elastostatics using Spherical Harmonics Extensions of Constrained Least-Squares for Obtaining Regularized Solutions to First-Kind Integral Equations Existence and Nonexistence Results for some Boundary Value Problems at Resonance Analytic Investigation of Thick Anisotropic Plates with Undulating Surfaces On Stokes Nonlinear Integral Wave Equation Dynamics of the Spurt Phenomenon for Single History Integral Constitutive Equations A Boundary Integral Equation Method for the Heat Equation Computational Simulation and Interfacial Shear Models for Downward Annular Wavy-Interface Condensing Flow in a Vertical Pipe Compact Fourth-Order Approximation for a Nonlinear Reaction-Diffusion Equation arising in Population Genetics Dynamic Deformation of a Layered Continuum Surrounding a Cylindrical or Spherical Cavity Boundary Value Problems for Harmonic Vector Fields on Non-Smooth Domains The Oblique Derivative Problem for General Elliptic Systems in Lipschitz Domains Viscous Aerodynamic Optimal Design of Flying Configurations via an Enlarged Variational Method Interface Crack Problem for a Piecewise Homogeneous Anisotropic Plane Micromechanics of Heterogeneous Materials Admissibility and Optimal Control for Stochastic Difference Equations Linear and Sublinear Tricomi via DFI Multidimensional Fractional Integrals on Spaces of Smooth Functions Piecewise Polynomial Projection Methods for Nonlinear, Multidimensional, Weakly Singular Integral Equations Asymptotics and Inequalities for a Class of Infinite Sums A New Theorem Concerning the Buckingham-Rayleigh Methods and General Dimensional Analysis Energy Decay for a Weak Solution of the Non-Newtonian Fluid Equations with Slowly Varying External Forces An Integral Representation for the Solution of 2-D Non-Stationary Flow of Micropolar Fluids A Monotonically Convergent Adaptive Method for Nonlinear Combustion Problems Stationary Oscillations of Elastic Plates with Robin Boundary Conditions Adapter and Driver Design for Rotary Encoders Expert System Design for Fault Diagnosing in CNC Machine Tools Non-Ideal Liquid Solutions Modeling by means of Integral Methods Symmetry Groups, Conservation Laws, and Group-Invariant Solutions of the Marguerre-von Karman Equations Modeling the Motion of an Underwater Explosion Bubble On some New Systems of N-ary Integral Equations Computational Simulations and Flow Domain Classification for Laminar/Laminar annular/Stratified Condensing Flows

The boundary integral equation method in plane elasticity

The boundary integral equation method in terms of real variables is applied to solve the interior and exterior Dirichlet and Neumann problems of plane elasticity. In the exterior case, a special far-field pattern for the displacements is considered, without which the classical scheme fails to work. The connection between the results obtained by means of this technique and those of the direct method is indicated.

Oscillation problems in thin plates with transverse shear deformation

In this paper, the authors present a modern theory of thin elastic plates with transverse shear deformation where the disturbance is represented by a train of harmonic waves. Dirichlet- and Neumann-type problems are formulated together with appropriate radiation conditions (in the case of the exterior domain). The paper shows that uniqueness for exterior problems is guaranteed for a range of flexural waves. In the interior problems, the presence of eigenfrequencies means that there is no general uniqueness result. The paper also indicates how corresponding results can be proved for micropolar plates.

On integral solutions of the equations of thin plates

A special constant matrix is constructed for every smooth closed boundary curve, whose non-singularity is a necessary and sufficient condition for the solubility by the direct method of the Dirichlet problem for the equations of bending of elastic plates.

On the solution of the Dirichlet problem for the two-dimensional Laplace equation

The solution of the Dirichlet problem for the two-dimensional Laplace equation is obtained as a modified single layer potential by a method applicable even when the logarithmic capacity of the boundary curve is equal to 1

On the Dirichlet Problem for the Two‐dimensional Biharmonic Equation

Modified fundamental solutions are used to show that the system of boundary integral equations in a direct method for the interior Dirichlet problem for the two-dimensional biharmonic equation has at most one solution on any smooth closed boundary contour.

Existence theorems in the theory of bending of micropolar plates

Abstract The existence is investigated of regular solutions of Dirichlet and Neumann boundary value problems by means of the boundary integral equation method in the theory of bending of thin micropolar plates.

THE CAUCHY PROBLEM IN THE THEORY OF PLATES WITH TRANSVERSE SHEAR DEFORMATION

The Cauchy problem for an infinite plate with transverse shear deformation is studied by means of an area potential and some special initial potentials. This is a fundamental step in the construction of the potential theory for dynamic problems for plates, since such results make it possible to reduce various initial-boundary value problems for the equations of motion to analogous ones for the homogeneous system, which can then be solved by means of retarded potentials.

Boundary Integral Equations in Dynamic Problems for Elastic Plates

Initial-boundary value problems with Dirichlet and Neumann conditions arising in the theory of bending of plates with transverse shear deformation are reduced to time-dependent boundary integral equations by means of layer potentials. The solvability of these equations is then investigated in Sobolev-type spaces.

Integral representations of the solutions for a bending plate on an elastic foundation

SummaryThe existence of distributional solutions is investigated for boundary integral equaitons associated with the bending of an elastic plate with transverse shear deformation on an elastic foundation.