Effect of gravity on visco-elastic surface waves in solids involving time rate of strain and stress of higher order.
Effect of imperfections and damping on the type of nonlinearity of circular plates and shallow spherical shells.
Effect of rotation and relaxation times on plane waves in generalized thermo-visco-elasticity.
Effect of rotation on wave propagation in a transversely isotropic medium.
Effective and homogenized coefficients
Effective computation of restoring force vector in finite element method
We introduce a new way of computation of time dependent partial differential equations using hybrid method FEM in space and FDM in time domain and explicit computational scheme. The key idea is quick transformation of standard basis functions into new simple basis functions. This new way is used for better computational efficiency. We explain this way of computation on an example of elastodynamic equation using quadrilateral elements. However, the method can be used for more types of elements and...
Effective energy integral functionals for thin films with bending moment in the Orlicz-Sobolev space setting
In this paper we deal with the energy functionals for the elastic thin film ω ⊂ ℝ² involving the bending moments. The effective energy functional is obtained by Γ-convergence and 3D-2D dimension reduction techniques. Then we prove the existence of minimizers of the film energy functional. These results are proved in the case when the energy density function has the growth prescribed by an Orlicz convex function M. Here M is assumed to be non-power-growth-type and to satisfy the conditions Δ₂ and...
Effective energy integral functionals for thin films with three dimensional bending moment in the Orlicz-Sobolev space setting
In this paper we consider an elastic thin film ω ⊂ ℝ² with the bending moment depending also on the third thickness variable. The effective energy functional defined on the Orlicz-Sobolev space over ω is described by Γ-convergence and 3D-2D dimension reduction techniques. Then we prove the existence of minimizers of the film energy functional. These results are proved in the case when the energy density function has the growth prescribed by an Orlicz convex function M. Here M is assumed to be non-power-growth-type...
Effective media for periodic anisotropic systems
Effects of In-plane Elastic Stress and Normal External Stress on Viscoelastic Thin Film Stability
Motivated by recent experiments on the electro-hydrodynamic instability of spin-cast polymer films, we study the undulation instability of a thin viscoelastic polymer film under in-plane stress and in the presence of either a close by contactor or an electric field, both inducing a normal stress on the film surface. We find that the in-plane stress affects both the typical timescale of the instability and the unstable wavelengths. The film stability...
Effects of variations in nonlinear damping coefficients on the parametric vibration of a cantilever beam with a lumped mass.
Efficient application of e-invariants in finite element method for an elastodynamic equation
We introduce a new efficient way of computation of partial differential equations using a hybrid method composed from FEM in space and FDM in time domain. The overall computational scheme is explicit in time. The key idea of the suggested way is based on a transformation of standard basis functions into new basis functions. The results of this matrix transformation are e-invariants (effective invariants) with such suitable properties which save the number of arithmetical operations needed for a...
Efficient inexact Newton-like methods with application to problems of the deformation theory of plasticity
Newton-like methods are considered with inexact correction computed by some inner iterative method. Composite iterative methods of this type are applied to the solution of nonlinear systems arising from the solution of nonlinear elliptic boundary value problems. Two main quastions are studied in this paper: the convergence of the inexact Newton-like methods and the efficient control of accuracy in computation of the inexact correction. Numerical experiments show the efficiency of the suggested composite...
Efficient representations of Green’s functions for some elliptic equations with piecewise-constant coefficients
Convenient for immediate computer implementation equivalents of Green’s functions are obtained for boundary-contact value problems posed for two-dimensional Laplace and Klein-Gordon equations on some regions filled in with piecewise homogeneous isotropic conductive materials. Dirichlet, Neumann and Robin conditions are allowed on the outer boundary of a simply-connected region, while conditions of ideal contact are assumed on interface lines. The objective in this study is to widen the range of...
Eigenfrequencies of generally restrained beams.
Eigenvalue approximations by mixed methods
Eigenvalue formulas for the uniform Timoshenko beam: the free-free problem.
Eigenvalue problem and unbounded connected branch of positive solutions to a class of singular elastic beam equations.
Ein Gewisses Randproblem aus der Theorie der Wärmeleitfähigkeit
Elastic behavior of a two--dimensional lattice beam.