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Leon Simula

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Papers by Leon Simula

Research paper thumbnail of Some recent developments of the homogenization theory with applications

This thesis in applied mathematics is devoted to theoretical and some of the numerical aspects of... more This thesis in applied mathematics is devoted to theoretical and some of the numerical aspects of the homogenization theory. The thesis consists of five papers. In the first paper we give a brief p ...

Research paper thumbnail of On stiffness properties of square honeycombs and other unidirectional composites

Composites Part B-engineering, 2001

In this paper we consider stiffness properties of square symmetric unidirectional two-phase compo... more In this paper we consider stiffness properties of square symmetric unidirectional two-phase composites with given volume fractions. First, we compare the effective moduli of the stiffest possible (or softest possible) of such materials which satisfy transverse isotropy or square isotropy with that of materials satisfying 3D-isotropy.

Research paper thumbnail of A new method for numerical solution of checkerboard fields

Journal of Applied Mathematics, 2001

We consider a generalized version of the standard checkerboard and discuss the difficulties of fi... more We consider a generalized version of the standard checkerboard and discuss the difficulties of finding the corresponding field by standard numerical treatment. A new numerical method is presented which converges independently of the local conductivities.

Research paper thumbnail of Some Methods for Calculating Stiffness Properties of Periodic Structures

Applications of Mathematics, 2003

We present a general numerical method for calculating effective elastic properties of periodic st... more We present a general numerical method for calculating effective elastic properties of periodic structures based on the homogenization method. Some concrete numerical examples are presented.

Research paper thumbnail of Some recent developments of the homogenization theory with applications

This thesis in applied mathematics is devoted to theoretical and some of the numerical aspects of... more This thesis in applied mathematics is devoted to theoretical and some of the numerical aspects of the homogenization theory. The thesis consists of five papers. In the first paper we give a brief p ...

Research paper thumbnail of On stiffness properties of square honeycombs and other unidirectional composites

Composites Part B-engineering, 2001

In this paper we consider stiffness properties of square symmetric unidirectional two-phase compo... more In this paper we consider stiffness properties of square symmetric unidirectional two-phase composites with given volume fractions. First, we compare the effective moduli of the stiffest possible (or softest possible) of such materials which satisfy transverse isotropy or square isotropy with that of materials satisfying 3D-isotropy.

Research paper thumbnail of A new method for numerical solution of checkerboard fields

Journal of Applied Mathematics, 2001

We consider a generalized version of the standard checkerboard and discuss the difficulties of fi... more We consider a generalized version of the standard checkerboard and discuss the difficulties of finding the corresponding field by standard numerical treatment. A new numerical method is presented which converges independently of the local conductivities.

Research paper thumbnail of Some Methods for Calculating Stiffness Properties of Periodic Structures

Applications of Mathematics, 2003

We present a general numerical method for calculating effective elastic properties of periodic st... more We present a general numerical method for calculating effective elastic properties of periodic structures based on the homogenization method. Some concrete numerical examples are presented.

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