Applied Mechanics and Materials Vol. 769

Abstract: In this paper we shall deal with application of analytical and numerical calculation methods in selected geotechnical problem. It is well-known that numerical modeling by Finite Element Method (FEM) is often used for solving complicated engineering problems. FEM is very universal and efficient tool for their solution. In our case a contact task of rigid shallow (circular, rectangular and strip) foundations loaded by centric force, has been solved. The obtained results of vertical normal stresses distributions according to analytical methods and FEM solutions have been analyzed and mutually compared. Results of the calculations have been presented in graphical and tabular form, too.

Abstract: This paper presents an analysis of a pile loaded in its head by a horizontal force. The pile crosses subsoil layers of a low bearing capacity and the bearing gravel layer below it. Further an analysis of displacements and internal forces of a bended pile in interaction with the layered subsoil, having various physical properties, is performed.

Abstract: The paper deals with the effect of non-uniform temperature over the cross-section in the steel frame structure under fire loading. The unequal temperature distribution causes additional bending moments in statically indeterminate structures. Numerical results of thermal and structural analysis from the commercial computer software ANSYS are compared with the experimental measurements on the steel frame exposed to high temperature.

Abstract: This paper deals with static analysis of load-bearing steel grid of a transparent roof. Ten structures with various spans (from 12.58 m to 30.08 m) and different heights (from 2.494 m to 7.471 m) have been modelled and analysed. The calculations were repeated for two common used types of the cross-sections - (60 x 40) mm and (60 x 60) mm. Permanent loads (the self-weight, the weight of glass panels) and variable loads (snow, wind) were taken into account. Obtained results were verified by four additional structures. The architects can use resultant graphs (the dimensions, maximum axial forces and maximum vertical displacements) in first stage of the design.

Abstract: This paper deals with the design optimization, static, modal and probability analyses of a simplified space truss, which was used to cover a festival square. Design optimization was used to achieve the best parameters for steel tubes of 3-D lattice plate. The results from two optimization methods were compared and finally modal analysis was performed with best parameters giving the own shapes and own frequencies. For the deterministic analysis the Monte Carlo simulation was used. Finally some results are presented.

Abstract: This paper deals with some problem on thickness of a plate rested on Winkler ́s foundation using the first order optimization method, while maintaining different restrictive conditions. The optimization analysis is based on a reduction of the thickness in the individual points. The aim is to obtain a minimum volume of the foundation plate. Finally some results of optimal design are presented.

Abstract: Von Misses truss is one of the best examples to explain different theoretical approaches, nature of non-linear solution, define the snap-through, illustrate interactive buckling, etc. The presented paper compares two nonlinear approaches to the problem. Effect of nonlinear terms in strain-displacement relationship on the load level in critical point of nonlinear solution is analyzed. To obtain the nonlinear equilibrium paths, the Newton-Raphson iteration algorithm is used. Corresponding levels of the total potential energy are defined. The peculiarities of the effects of the initial imperfections are investigated. Custom FEM computer program has been used for analysis. Full Newton-Raphson procedure, in which the stiffness matrix is updated at every equilibrium iteration, has been applied. Obtained results are compared with results of the nonlinear analysis using ANSYS system, element type BEAM3 is used. The arc-length method is chosen for analysis, the reference arc-length radius is calculated from the load increment. Only fundamental path of nonlinear solution has been presented.

Abstract: Deformations of an I-section steel beam under equal end moments are studied in this article. Initial geometric imperfection of the beam axis was introduced according to the Eurocode standard. Numerical studies have shown that the lateral deflection of slender beams under major axis bending can be relatively high. The acceptability of high values of lateral deflections within the framework of the serviceability limit state is discussed. In the next part of the paper, the limit value of maximum deflection was introduced as a fuzzy number. Fuzzy analysis of the maximum moment, which causes maximum deflection, was performed. The slenderness values of beams for which the serviceability limit state is the limiting condition for design were identified.

Abstract: The paper deals with the designing and analysing of concrete structures. A particular attention is paid to a multi-segment slab made from reinforced concrete. The purpose of the paper is to evaluate, in a non-linear analysis, impacts of input parameters of the concrete on the real load-carrying capacity of the ceiling which has been designed originally in DeMKP. FEM software applications have been used in the analysis. This is an in-house application DeMKP for designing the systems in line with standardised procedures. Another software is ATENA Science which can be used for non-linear analyses.

Abstract: The presented paper delas with constitutive equations of the linear theory of viscoelasticity. The integral representations for homogeneous isotropic medium located in isothermal conditions are introduced. Relations are derived for the relaxation and creep processes, as well as relations between these functions in the Laplace images. In the solution we assume quasi-static external force loading under which the analyzed viscoelastic body in each time t shows infinitesimal deformations. General isotropic tensor of fourth degree G_ijkl (t) we use to derive the relationship between deviator stress and deformation, as well as the relations between stresses and distortions that produce volumetric changes. It is shown that for the linear viscoelastic problem can be used Stieltjes convolution and its algebraic properties. Derived relations and procedures followed to the results of differential-operator's representation of constitutive equations of linear viscoelasticity theory that have been published in the previous work of Authors.