Bicriterion optimization of cold-formed thin-walled beams with I-type shape

The work is devoted to bi-criterion optimization of thin-walled cold-formed beams under pure bending. The first objective function is the area of a beam cross-section and the maximum deflection of a beam is taken as the second one. The strength and stability constraints in bi-objective optimization problem are taken into account and formulated analytically. Some results of numerical calculations are presented in the form of the tables. (© 2005 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

SBFEM elements for thin-walled composite beams with arbitrary layup

The scaled boundary finite element method (SBFEM) is a semi-analytical method in which only the boundary is discretized. The results on the boundary are scaled into the domain with respect to a scaling center which must be “visible” from the whole boundary. For beam-like problems the scaling center can be selected at infinity and only the cross-section is discretized. Two new elements for thin-walled beams have been developed on the basis of the first order shear deformation theory. The beam sections are considered to be multilayered laminate plates with arbitrary layup. The arbitrary cross-section is discretized with beam elements of Timoshenko type. Using the virtual work principle gives the SBFEM equation, which is a system of differential equations of a gyroscopic type. The solution is calculated using the matrix exponential function. The elements have been tested and compared with a finite element model and they give good results. (© 2014 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Optimization of open cross sections of thin-walled beams with plate-shell-flanges

The paper is devoted to a monosymetrical cold-formed thin-walled beam with open cross section. Its flange consists of plates and circular shells. The beam is under pure bending. The cross section is characterized by dimensionless parameters. The authors are searching for an optimal cross section shape of considered beam. This optimal shape is determined by means of parametric optimization. The dimensionless objective function is so defined as to comprise both cross section area and a maximal allowable bending moment. The constraints follow from the local buckling conditions and geometric restrictions. Moreover, there are optimized cross sections of beams, for which the shear center is located either in the web or in the centroid of the cross section. Results are compared and analyzed. (© 2005 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Elactic buckling of thin-walled beams with sandwich and double bends flanges

This of the paper are two thin–walled beams with sandwich and double bends flanges. Cross section of these beams is of C type. The beams are simply supported and subjected to a couple of moment – the pure bending. Geometric propeties (warping functions and inertia moments) of two sections with sandwich and double bendsflanges are separately described by dimensionless parameters. Values of critical loads for family of thin–walled beams are numerically determined on the ground of analytical solution. A comparative analysis for selected beams with the use of FEM is performed. Morover the values of critical loads for a family of thin–walled beams are experimentally researched in the Material Strength Laboratoey of the Poznan University of Technology. Finally, the results of the investigation for thin–walled beams are compared in paper. Results of the calculation are presented in tables and figures. (© 2008 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Strengthening of RC beams with an innovative timber-FRP composite system

The results of a theoretical and experimental research project on the use of an innovative technique for strengthening concrete beams are presented. A spacer element is inserted between the tension side of a beam and the composite material to increase its lever arm and to enhance the over all stiffness of the strengthened beam. The main aim of this exploratory project was to increase the ultimate failure load of strengthened beam specimens, whilst guaranteeing acceptable over all deflections at the serviceability limit states. This resulted into a significant reduction in the amount of FPR required and in a better utilization of the materials employed. A preliminary theoretical study was carried out to investigate the effect of Young’s modulus, failure strain, and thickness of the element to be used as a spacer in order to determine the best possible candidate material. Three tests on 2.5-m-long beams were carried out, and different anchorage techniques were used to try and prevent the debonding of the strengthening system. The results from this pilot study are very promising, as the strengthening system ensures an adequate initial stiffness along with an improved ultimate flexural capacity. Russian translation published in Mekhanika Kompozitnykh Materialov, Vol. 44, No. 3, pp. 403–416, May–June, 2008.     

Mixed finite element models for free vibrations of thin-walled beams

Simple mixed finite element models are developed for the free vibration analysis of curved thin-walled beams with arbitrary open cross section. The analytical formulation is based on a Vlasov's type thin-walled beam theory which includes the effects of flexural-torsional coupling, and the additional effects of transverse shear deformation and rotary inertia. The fundamental unknowns consist of seven internal forces and seven generalized displacements of the beam. The element characteristic arrays are obtained by using a perturbed Lagrangian-mixed variational principle. Only C⁰ continuity is required for the generalized displacements. The internal forces and the Lagrange multiplier are allowed to be discontinuous at interelement boundaries.

Numerical results are presented to demonstrate the high accuracy and effectiveness of the elements developed. The standard of comparison is taken to be the solutions obtained by using two-dimensional plate/shell models for the beams.     

Asymptotic analysis of Poisson's equation in a thin domain and its application to thin-walled elastic beams and tubes

We study the limit behaviour of solution of Poisson's equation in a class of thin two-dimensional domains, both simply connected or single-hollowed, as its thickness becomes very small. The method is based on a transformation of the original problem into another posed on a fixed domain, obtention of a priori estimates and convergence results when thickness parameter tends to zero. As an important application of abstract results we obtain the limit expressions for functions appearing in elastic beam theories as torsion and warping functions. In this way, we provide a mathematical justification and a correct definition of torsion, warping and Timoshenko functions and constants that should be used in the open and closed thin-walled elastic beam theories. © 1998 by B. G. Teubner Stuttgart–John Wiley & Sons Ltd.     

Exact solutions for coupled analysis of thin-walled functionally graded beams with non-symmetric single- and double-cells

In the present work, the exact solutions for coupled analysis for bending and torsional case thin-walled functionally graded (FG) beams with non-symmetric single- and double-cells are presented for the first time. For this purpose, an accurate and efficient method is proposed to obtain the FG member stiffness matrix based on the series expansions of displacement components. Three types of material distributions are considered and the beam mechanical properties are graded along the wall thickness according to a power law of the volume fraction. The present beam model is on the basis of the Euler-Bernoulli beam theory and the Vlasov one for bending and torsional problems, respectively. The explicit expressions for displacement parameters are derived using the power series approach from the four coupled equilibrium equations. Finally, the FG member stiffness matrix is determined from the seven force-displacement relations. In order to show the accuracy and super convergence of the thin-walled FG beam element developed by this study, the numerical solutions are presented and compared with results obtained from the finite beam element based on the approximate interpolation polynomials and other available results. Especially, the effects of various structural parameters such as material distribution type, volume fraction index, boundary condition, and material ratio on the spatially coupled responses of FG box beams with non-symmetric single- and double-cells are parametrically investigated.     

Simulation of ECB decisions and forecast of short term Euro rate with an adaptive fuzzy expert system

The elaboration of optimal monetary policy strategies, and the statistical estimation of monetary policy rules followed by European Central Bank (ECB) in the new currency area of the Euro, are difficult to follow with the standard statistical models. For this reason we have developed an adaptive fuzzy expert system in order to mimic the framework on which the monetary policy strategy of the ECB is based. The expert system knowledge base consists of a set of fuzzy and crisp rules located at two different hierarchical levels. The high-level of the system receives some intermediate output values from the low-level and processes this information by means of a set of crisp rules. The low-level prepares these intermediate output values with the use of a fuzzy inference engine applied to economic input variables. The use of an expert system allows for modelling the ECB behaviour with the use of wider scope of knowledge, when compared with more traditional computational techniques. Rules at different hierarchical levels and at different intra-level groups, allow for managing the potentially contradictory structure of the ECB strategy. The system has been tested on the economic and financial time series going from the January 1999 to September 2000. The system’s correct prediction was estimated to overall 70% and, considering the complexity of the task, the results obtained are promising.     

Design of closed thin-walled composite shapes for bending

A study is made of the possibility of dividing the complex bending of a structure into elementary components, and an examination is made of closed wing-type monocoque structures with a rigid contour. The structures studied are asymmetric with respect to their geometric and stiffness characteristics. They are subjected to bending without torsion and are referred to a cylindrical coordinate system (Z, S). The longitudinal displacements are determined on the basis of the method of conjugate displacements by integrating the Cauchy equation and circulation equation, with the displacement along the contour (due to its stiffness) being represented in the form of a series containing terms describing the bending of the structure. The shear strains are similarly represented. The resolvent equations are obtained by using the principle of the minimum potential strain energy of the contour.Deceased.Moscow State Aviation Institute (Technical University). Translated from Mekhanika Kompozitnykh Materialov, No. 1, pp. 82–89, January–February, 1997.     

A fuzzy knowledge base of an expert system for analysis of manual lifting tasks

Development of the fuzzy knowledge base of an expert system for analysis of manual lifting tasks (liftan) is described. The system, written in Maclisp and implemented on a DEC-10 mainframe computer, allows a non-expert in the field to utilize the relevant knowledge and apply it to analyze specific work situations. The knowledge base of liftan consists of 85 rules related to risk analysis and 64 rules used to create explanations and messages to the user. The values of the variables used in the fuzzy knowledge base are represented using the linguistic approach. In order to illustrate the practical implementation of the developed knowledge base, an example is shown.     

Integration of production planning and scheduling using an expert system and a genetic algorithm

In the traditional approaches, processes of planning and scheduling are done sequentially, where the process plan is determined before the actual scheduling is performed. This simple approach ignores the relationship between the scheduling and planning. Practical scheduling systems need to be able to react to significant real-time events within an acceptable response time and revise schedules appropriately. Therefore, the author proposes a new methodology with artificial intelligence to support production planning and scheduling in supply net. In this approach, the production planning problem is first solved, and then the scheduling problem is considered with the constraint of the solution. The approach is implemented as a combination of expert system and genetic algorithm. The research indicates that the new system yields better results in real-life supply net than using a traditional method. The results of experiments provide that the proposed genetic algorithm produces schedules with makespan that is average 21% better than the methods based on dispatching rules.     

Behavior of Gaussian beams in an anisotropic medium with interface

A region that consists of two parts with anisotropic Riemannian metrics is considered. The metric has a jump on the interface. Asymptotic solutions of the wave equation, reflected and transmitted from the interface, i.e., Gaussian beams (“quasiphotons”), are constructed. Bibliography: 7 titles. __________ Translated from Zapiski Nauchnykh Seminarov POMI, Vol. 324, 2005, pp. 77–109.