### Contents of Journal of Mechanical Engineering *54,* 4 (2003)

HOSCHL, C., OKROUHLIK, M.: Solution of systems of nonlinear equations 197
HALAJ, M.: A contribution to calibration of piezoresistive tactile
matrix sensors 228
MURIN, J.: Beam element with varying stiffness 239

# Abstracts

###
Solution of systems of nonlinear equations

CYRIL HOSCHL, MILOSLAV OKROUHLIK

Numerical methods suitable for the solution of nonlinear problems are treated
with intention to elucidate their foundations and motivations. The presented
paper is intended to serve as an introduction to a more profound study of
these methods. A more detailed analysis could be found in cited references.
The Nedler-Mead simplex method, the Newton-Raphson method and its
modifications, the method of the steepest descent, the method of conjugate
directions or gradients and quasi-Newton methods are described with a special
attention paid to the last ones.

###
A contribution to calibration of piezoresistive tactile matrix sensors

MARTIN HALAJ

Calibration of the tactile matrix sensor represents a complex problem with
highly interesting mathematical solution. Due to big complexity of the
calibration model, describing sensor behavior during calibration, several
numerical problems occur. As the complexity of calibration model must reflect
all important features of the sensor that could affect the calibration result,
some of the calculations during calibration seem to be of utmost difficulty.
Therefore, a two-step approach is adopted, enabling simplification of several
model elements.

###
Beam element with varying stiffness

JUSTIN MURIN, VLADIMIR KUTIS

The stiffness matrix of a new 3D Euler-Bernoulli beam element (involving the
1st- and 2nd-order beam theory, and St. Venant torsion) with continuously
changing elasticity modulus and cross-section characteristics (cross-sectional
area and moments of inertia) along its longitudinal axis is proposed in this
article. The stiffness matrix can be established using the direct stiffness
method or new shape functions that are derived in this contribution, too. The
stiffness matrix involves transfer constants that depend on the stiffness
variation (1st-order theory) and the axial force (2nd-order theory). The
transfer constants are derived using a simple numerical algorithm. The results
of the numerical experiments prove the effectiveness and accuracy of the
developed element. It follows from these results that our beam element fulfils
equilibrium equations in the global and local sense, and the accuracy of the
results does not depend on the fineness of the mesh.