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.

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 Miura-ori 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 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.

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.

A four-noded finite element of a moderately thick plate made of functionally graded material (FGM) is presented. The base element is rectangular and can be extended to any shape using a transformation based on NURBS functions. The proposed 2D shape functions are consistent with the physical interpretation and describe the states of element displacement caused by unit displacements of nodes. These functions depend on the FGM’s material parameters and are called material-oriented. The shape function matrix is based on a superposition displacement field of two plate strips with 1D exact shape functions. A characteristic feature of the proposed formulation is full coupling of the membrane and bending states in the plate. The analytical form of the stiffness matrix and the nodal load vector was obtained, which leads to the numerical efficiency of the formulation. The element has been incorporated into Abaqus software with the use of Maple program. The finite element shows good convergence properties for different FGM models in the transverse direction to the middle plane of the plate. During derivation of the 2D plate element the formally exact 1D finite element for transverse nonhomogeneous FGM plate strip was developed.

The present paper discusses an innovative approach providing the solution sets of engineering structures with uncertain parameters. The approach is based on the properties of convex sets and can be applied to structures described by the system of algebraic equations. The present paper focuses on trusses and frames applications, but in general it can be applied to various structures made of thin and thick bars and some plate and shell problems. The uncertain parameters are assumed to be independent. In addition, calculations are valid for any level of uncertainty and the obtained solution sets are exact within the assumed theory and are insensitive for perturbed data. Furthermore, solutions obtained by the present approach can be considered as benchmark solutions and can be used as a reference for other algorithms. The presented formulae allow the analysis of the influence of uncertain parameters on the behaviour of the structure. The presented considerations are illustrated by calculation of two truss examples.