The initial post-buckling behaviour of a cold-formed channel member flange after its local buckling is investigated. An axially compressed column or beam subjected to pure bending is considered. The member material is assumed to follow a linear stress-strain relationship. The governing non-linear differential equation of the problem is derived using the minimum total potential energy principle. An approximate solution for the equation is found by means of the perturbation approach, which allows obtaining the critical buckling stress and the initial post-buckling equilibrium path. The bifurcation point is shown to be symmetric and stable. The proposed analytical solution is compared with finite element method (FEM) and finite strip method (FSM) results to check the validity and range of applicability.
Distortional buckling of axially compressed columns of box-like composite cross sections with andwithout internal diaphragms is investigated in the framework of one-dimensional theory. The channel membersare composed of unidirectional fibre-reinforced laminate. Two approaches to the member orthotropic materialare applied: homogenization based on the theory of mixture and periodicity cells, and homogenization basedon the Voigt–Reuss hypothesis. The principle of stationary total potential energy is applied to derive thegoverning differential equation. The obtained buckling stress is valid in the linear elastic range of columnmaterial behaviour. Numerical examples address simply supported columns, and analytical critical stressformulas are derived. The analytical and FEM solutions are compared, and sufficient accuracy of the resultsis observed.
The paper includes a case study of modelling a real historic church using the finite element method (FEM) based on laser scans of its geometry. The main goal of the study was the analysis of the causes of cracking and crushing of masonry walls. An FEM model of the structure has been defined in ABAQUS. A non-linear dynamic explicit analysis with material model including damage plasticity has been performed. A homogenization procedure has been applied to obtain the material parameters used in the modelling of masonry. In the numerical analysis, the interactions between the church structure, the foundations and the ground were taken into account. The obtained results match well with the damaged area of the entire structure from the in-situ survey, and it should be highlighted that the proposed FEM model allows for a rather precise identification of the causes and effects of cracking walls in a qualitative sense. Also a brief research summary is presented.
The paper concerns flexural buckling and initial post-buckling of axially compressed columns made of aluminium alloy described by the Ramberg-Osgood relationship. The non-linear differential equation of the problem is derived using the stationary total energy principle and the assumptions of classical beam theory within a finite range. The approximate analytical solution of the equation leading to the buckling loads and initial post-buckling equilibrium path is determined by means of the perturbation approach. Numerical examples dealing with simply supported and clamped I-columns are presented, the effect of the material non-linearity on the critical loads and initial post-buckling behaviour in comparison to linear one is discussed too. The analytical results are compared with the FEM solutions to present a good agreement.
This book commemorates the 80th birthday of Prof. W. Pietraszkiewicz, a prominent specialist in the field of general shell theory. Reflecting Prof. Pietraszkiewicz’s focus, the respective papers address a range of current problems in the theory of shells. In addition, they present other structural mechanics problems involving dimension-reduced models. Lastly, several applications are discussed, including material models for such dimension-reduced structures.
The article reviews a number of papers in the light of buckling analy- sis of thin-walled columns and beams. Stability of thin-walled columns and beams are considered a vital engineering science issue in both historical and present-day approaches. The paper refers to the recent authors’ works of the 2012–2019 period, published in leading journals. Similar review of stability problems of thin-walled structures developed at Gdansk University of Technology is published in Szymczak (A review of stability problems of thin-walled structures developed at Gdansk Uni- versity of Technology, 69–78, 2003, ), Szymczak (Selected problems of stability of thin-walled columns with bisymmetric cross-section, 111–128, 2012, ). This paper is a continuation of the earlier reviews. Only selected references are given.
The paper concerns first order sensitivity analysis of flexural and torsional bucklin g loads of axiallycompressed thin-walled columns with bisymmetric or axisymmetric cross-section made of unidirectional fibre-reinforcedlaminate. The first variation of critical loads versus some variations of the column material properties and cross-sectionaldimensions is derived. Numerical examples dealing with simply supported I-columns are presented. The distributions ofsensitivity functions of critical loads are presented with respect to variations of the parameters assumed along the columnaxis are shown. Some differences between sensitivity functions of both kinds of buckling are described and accuracy ofsensitivity analysis in assessment of the critical buckling load changes due to some variations of the column parameters is discussed.
In this paper a research towards understanding of mechanics of ventral hernia operated with the use of Physiomesh Open image in new window implant and SecureStrap Open image in new window staples is described. Experimental and numerical studies are conducted for that purpose. Experimental works cover uni-axial tension tests of the implant samples and of the implant-staples-tissue system. Also experiments on implant-staples-tissue models, representing operated hernia, subjected to impulse pressure loading are performed. Based on that, constitutive model of the mesh has been identified and failure load of the staples has been determined. In the experiments on the operated hernia systems subjected to pressure loading safe loading level has been determined and failure modes connected to higher pressure values have been observed. Finally, in the numerical simulations of the operated hernia model, built according to FEM rules, it has been proved that failures observed experimentally result from exceeding of the load bearing capacity of the staples considered in this study.
The investigation concerns local buckling of compressed flanges of axially compressed composite channel columns. Cooperation of the member flange and web is taken into account here. The buckling mode of the member flange is defined by rotation angle a flange about the line of its connection with the web. The channel column under investigation is made of unidirectional fibre-reinforced laminate. Two approaches to member orthotropic material modelling are performed: the homogenization with the aid of theory of mixture and periodicity cell or homogenization upon the Voigt–Reuss hypothesis. The fundamental differential equation of local buckling is derived with the aid of the stationary total potential energy principle. The critical buckling stress corresponding to a number of buckling half-waves is assumed to be a minimum eigenvalue of the equation. Some numerical examples dealing with columns are given here. The analytical results are compared with the finite element stability analysis carried out by means of ABAQUS software. The paper is focused on a close analytical solution of the critical buckling stress and the associated buckling mode while the web–flange cooperation is assumed.
The paper deals with local buckling of a compressed single flange of thin-walled channel cold- formed columns and beams made of aluminum alloy. Material is described by means of the Ramberg-Osgood constitutive equation. Axial compression of the columns and beams undergoing bending is taken into consid- eration. A simple model of the member flange in the form a long beam elastically connected to the web is used to find the critical buckling stress. The governing differential equation is derived with the aid of the sta- tionary total potential energy principle. The tangent modulus theory is applied to find the critical buckling stress and buckling modes. Analytical formulas of the critical stress and buckling mode are positively verified by the FEM and FSM analysis of numerical examples.