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


Solution of systems of nonlinear equations


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


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


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.