The paper is dedicated to the algebraic formulation of elastic frame equations. The obtained set of equations describe deformations of moderately thick frames made of both compressible and incompressible bars, grillages of rigid or pin-joined connections, and trusses. Plane as well as space structures are presented. The paper is an extension of the article of T. Lewiński written in 2001 related to thin bars. Algebraic equations with diagonal constitutive matrix are original and suitable for various engineering applications and for educational purposes.

The paper is dedicated to the numerical analysis of a single-step joint, enabling the prediction of stiffness and failure modes of both single- and double-step joints. An experimental analysis of the geometrically simplest version, the single-step joint, serves as a reference for the calibration of the subsequent finite element model. The inhomogeneous and anisotropic properties of solid timber make detailed modelling computationally intensive and strongly dependent on the respective specimen. Therefore, the authors present a strategy for simplified but still appropriate modelling for the prediction of local failure at certain load levels. The used mathematical approach is based on the linear elasticity theory and orthotropic material properties. The finite element calculations are performed in the environment of the software Abaqus FEA. The calibrated numerical model shows a good conformity until first failures occur. It allows for a satisfactory quantification of the stiffness of the connection and estimation of the force when local failure begins and is, therefore, recommended for future, non-destructive research of timber connections of various shapes.

Origami is an old art of paper folding. From mechanical point of view origami can be defined as a folded structure. In the present paper a comparative study of four origami inspired folded plate structures is presented. Longitudinal, facet, egg-box and Miuraori origami modules are used for the analysis. The models are based on six-parameter shell theory with the use of the finite element method. Convergence analysis of each module is presented. Numerical study of roof folded plates in oriented to the comparison of maximal displacements and stresses in the structures. Some parametric analysis is also presented.

The present paper is dedicated to the analysis of under sleeper pads (USP), which are resilient elements used in ballasted track systems as vibration isolators. Four types of USP are considered. The authors present the results of laboratory tests, which are then used as input values for the finite element (FE) and mechanical model of the structure. A special focus is put on the description of an original four-degree-of-freedom (4DoF) mechanical model of the system that includes a fractional rheological model of USP. Using the proposed approaches, the dynamic characteristics of under sleeper pads are determined, and conclusions on vibration isolation effectiveness are drawn.

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