Showing papers in "Journal of Theoretical and Applied Mechanics in 2004"

Elastic buckling of a porous beam

Abstract: The work deals with the problem a straight beam of a rectangular cross-section pivoted at both ends and loaded with a lengthwise compressive force. The beam is made of an isotropic porous material. Its properties vary through thickness of the beam. The modulus of elasticity is minimal on the beam axis and assumes maximum values at its top and bottom surfaces. The principle of stationarity of the total potential energy enables one to define a system of differential equations that govern the beam stability. The system is analytically solved, which leads to an explicit expression for the critical load of the compressed beam. Results of the solution are verified on an example beam by means of the Finite Element Method (COSMOS).

Factors effecting internal damping in aluminum

Abstract: The internal damping of metallic materials varies with many different environmental effects. These are the frequency, amplitude of strain or stress, and temperature. In addition, internal damping is effected by corrosion fatigue, grain size, and porosity. The damping also depends on the number of fatigue cycles. There is a functional relationship among the damping, number of cycles and applied stress. In this study, these seven different environmental factors and their effects on the damping are analysed in the case of 6061 aluminum alloy. The relationships between the damping and every single effective factor are complex and vary depending on the aluminum type.

Reliability based optimization of steel frames under seismic loading conditions using evolutionary computation

Abstract: Earthquake-resistant design of structures using probabilistic analysis and performance-based design criteria is an emerging field of structural engineering. These new analysis and design methodologies are aimed at improving the existing practice and design codes for better prediction of the structural performance. In this paper, a robust and efficient methodology is presented for performing reliability-based structural optimum design of steel frames under seismic loading. The optimization part is realised with evolution strategies, while the reliability analysis is carried out with the Monte Carlo simulation method incorporating the latin hypercube sampling technique for the reduction of the sample size. The probability of failure of the frame structures, in terms of interstorey drift limits, is determined via the multi-modal response spectrum analysis.

Biomechanical modelling for whole body motion using natural coordinates

Abstract: The study of spatial human movements requires the development and use of a three-dimensional model. The model proposed here has 44 degrees-of-freedom and it is described using natural coordinates, which do not require an explicit definition of rotation coordinates. The biomechanical model consists of 16 anatomical segments composed of 33 rigid bodies. Joint actuators are introduced into equations of motion of the multibody model by means of kinematic driver constraints in order to reflect the effect of the muscle forces about each anatomical joint. After associating a Lagrange multiplier to each joint actuator, the torques that represent muscle forces become coupled with the biomechanical model through the Jacobian matrix of the underlying multibody system. The developed model is applied to identify net torques and reaction forces at the anatomical joints in application cases that include the take-off to aerial trajectories and standing backwards somersault.

Multi-combinative strategy to avoid premature convergence in genetically-generated fuzzy knowledge bases

Abstract: A growing number of industrial fields is concerned by complex and multi-objective problems. For this kind of problems, optimal decision making is critical. Decision support systems using fuzzy logic are often used to deal with complex and large decision making problems. However the main drawback is the need of an expert to manually construct the knowledge base. The use of genetic algorithms proved to be an effective way to solve this problem. Genetic algorithms model the life evolution strategy using the Darwin theory. A main problem in genetic algorithms is the premature convergence, and the last enhancements in order to solve this problem include new multi-combinative reproduction techniques. There are two principal ways to perform multi-combinative reproduction within a genetic algorithm, namely the Multi-parent Recombination, Multiple Crossover on Multiple Parents (MCMP); and the Multiple Crossovers Per Couple (MCPC). Both techniques try to take the most of the genetic information contained in the parents. This paper explores the possibility to decrease premature convergence in a real/binary like coded genetic algorithm (RBCGA) used in automatic generation of fuzzy knowledge bases (FKBs). The RBCGA uses several crossover mechanisms applied to the same couple of parents. The crossovers are also combined in different ways creating a multiple offspring from the same parent genes. The large family concept and the variation of the crossovers should introduce diversity and variation in otherwise prematurely converged populations and hence, keeping the search process active.

Fuzzy reactive control of wheeled mobile robot

Abstract: This paper proposes a sensor based navigation method with a fuzzy combiner for navigation of a mobile robot in uncertain environments. We discuss a fuzzy approach to path design and control of simple individual behaviours of a wheeled mobile robot in an unknown 2D environment with static obstacles. A strategy of reactive navigation is developed including three main behaviours: reaching the middle of a collision-free space behaviour, goal-seeking behaviour and wall-following behaviour. These simple individual behaviours are achieved by means of fuzzy inference systems. It is assumed that each low-level behaviour has been well developed at the design stage and then fused by the fuzzy combiner of behaviours to determine proper actions acting on the environment at the running stage. The fuzzy combiner can fuse low-level behaviours so that the mobile robot can go for the goal position without colliding with obstacles. The fuzzy combiner is a soft switch that chooses more than one low-level action to be active with different degrees through fuzzy combination at each time step. The output of the navigation level is fed into a fuzzy tracking controller that takes into account the dynamics of the mobile robot. A computer simulation have been conducted to illustrate the performance of the proposed fuzzy combiner of behaviours by a series of experiments on an emulator of the wheeled mobile robot Pioneer-2DX.

Some methods for multicriteria design optimization using evolutionary algorithms

Abstract: In this paper new multicriteria design optimization methods are discussed. These methods are evolutionary algorithm based methods, and their aim is to make the process of generating the Pareto front very effective. Firstly, the multistage evolutionary algorithm method is presented. In this method, in each stage only a bicriterion optimization problem is solved and then an objective function is transformed to the constrain function. The process is repeated till all the objective functions are considered. Secondly, the preference vector method is presented. In this method, an evolutionary algorithm finds the ideal vector. This vector provides the decision maker with the information about possible ranges of the objective functions. On the basis of this information the decision maker can establish the preference vector within which he expects to find a preferred solution. For this vector, a set of Pareto solutions is generated using an evolutionary algorithm based method. Finally, the method for selecting a representative subset of Pareto solutions is discussed. The idea of this method consists in reducing the set of Pareto optimal solutions using the indiscernibility interval method after running a certain number of generations. To show how the methods discussed work each of them in turn is applied to solve a design optimization problem. These examples show clearly that using the proposed methods the computation time can be reduced significantly and that the generated solutions are still on the Pareto front.

Numerical investigation of a new type of artificial lumbar disc

Abstract: The replacement of a damaged lumbar disc by an artificial organ is still not satisfactorily solved problem of surgery. In the study, the finite element method together with CAD programs and experimental validation was used in investigations of a new type of artificial disc for lumbar spine. The presented 3D parametrical FE models take into account nonhomogenous properties of tissues, contact with friction between the parts of the analysed systems, large strains and large displacements. The stress analyses were performed for the prostheses being in clinical use and for some new designs. The conclusions concern most important determinants of the mechanical quality of the intervertebral disc prosthesis.

Vibration and stability of a column subjected to the generalised load by a force directed towards the pole

Abstract: A new loading of slender systems, which is a generalised load by a force directed towards the positive or negative pole, is presented in the paper. A new constructional scheme of the loading and receiving heads is introduced. Theoretical considerations connected with the formulation of boundary conditions are shown in this paper. Values of the critical force and the course of natural frequency in relation to the external load for given geometry and physical constants of the column are determined dependending on the constructional solution of the loading and receiving heads. The results of theoretical and experimental research are compared one with another.

Buckling of I-core sandwich panels

Abstract: Necessity of optimisation of ship hull structural mass calls for application of innovative materials and structural components. One option is based on using structural components with internal structure. The considered sandwich panels are composed of two plates stiffened by vertical ribs (I-core) or ribs of different shape (V-core). Such panels are applied as the ship hull structural components, replacing the conventional stiffened panels. They are subject to typical loadings acting in the ship hull; tension, compression and lateral loading. Analysis of stability of sandwich panels subject to compressive loading is presented in the paper. Stabilities of conventional and innovative ship panels were compared. Influence of the filling foam was also investigated.

Vibrations and stability of a two-rod column loaded by a sector of a rolling bearing

Abstract: In this work, a new type of loading of slender systems, which is a follower force directed towards a positive or a negative pole is presented. Constructional models of loading heads, which realize this type of loading, are also presented. The variant of theoretical investigations concerning formulation of boundary conditions is shown. It results from the energetic formulation. Dependently on constructional variants of both the loading and receiving heads, values of the critical force and courses of the natural frequency as a function of the external loading for the applied geometry and physical constants of the column are determined. Theoretical results are compared with those from an experiment.

A fatigue failure criterion for multiaxial loading with phase shift and mean value

Abstract: A new criterion based on the critical plane approach has been developed for multiaxial non-proportional fatigue failure. The criterion correctly takes into account the influence of phase shift and mean values under combined bending and torsion loading. From a certain point of view, the criterion with such a defined non-proportionality measure can be understood as a combination of the two approaches: critical plane and integral approach. The criterion has the following form $ \tau_{\alpha^*(eqnp)} = (\tau_{\alpha^*(a)} + c_1 \sigma_{\alpha^*(a)} + c_2\sigma_{\alpha^*(m)}) \Bigl(1 + \frac{t_{-1}}{b_{-1}}H^n\Bigr) \leq c_3 $ where the multiplicand of the equivalent shear stress $ \tau_{\alpha^*(eqnp)}$ contains the amplitude of the shear stress $ \tau_{\alpha^*(a)}$, the amplitude $ \sigma_{\alpha^*(a)}$ and mean value $ \sigma_{\alpha^*(m)}$ of the normal stress acting in the critical plane. The multiplier contains the loading non-proportionality measure $ H$. Taking into account the fact of different sensitivity of various materials to loading non-proportionality, the equation also includes the material data: $ t_{-1}$ – fatigue limit in torsion, $ b_{-1}$ – fatigue limit in bending. The predictive capability of the criterion was demonstrated by analyzing 67 experimental results from the literature. The predicted results are generally in good agreement with the experimental ones.

Neural network assisted crack and flow identification in transient dynamics

Abstract: Crack and flaw identification problems in two-dimensional elastomechanics are numerically studied in this paper The mechanical modelling is based on boundary element techniques, with special care of hypersingular issues for the cracks The possibility of partially or totally closed cracks (unilateral contact effects) is taken into account by linear complementarity techniques Backpropagation neural networks are used for the solution of the inverse problems For dynamical problems, a suitable preprocessing of the input data enhances the effectiveness of the procedure For the two-dimensional examples presented here, the proposed method has similar performance for classical crack and flaw identification problems The identification of unilateral cracks is a considerably more difficult task, which nevertheless, can also be solved by the same method, provided that a suitable dynamical test loading is applied

Fuzzy-neural and evolutionary computation in identification of defects

Abstract: It is known that an elastic body contains some internal defects such as voids, cracks, additional masses, etc. This paper is devoted to a method based on computational intelligence for non-destructive defect identification. In the presented paper, an elastic body loaded statically is considered. The body contains an unknown number of internal defects. There are a lot of applications based on non-destructive methods. The Evolutionary Algorithm (EA) with the Boundary Element Method (BEM) is a very effective tool in the identification of internal defects. In this method, the fitness function is calculated for each chromosome in each generation by the BEM. The number of chromosomes in each generation is quite large, and the number of generations is also large, so the time needed to carry out the identification is very long. Methods based on Artificial Neural Networks (ANN) find the position and shape of internal defects in a very short time. Because ANNs are usually trained using gradient methods, the risk that the solution is in a local optimum is one of disadvantages of such a method. There is also a problem when the ANN has to identify two or more different kinds of defects (cracks, voids and additional masses) in one body. In the presented method, an EA is connected with the ANN in one system. This operation allows to avoid main disadvantages of these methods and to use their advantages. The evolutionary algorithm is applied to identify the number of defects and their parameters (position and size). The identification of a defect in the body is performed by minimizing the fitness function which is calculated as a difference between measured and computed displacements in some sensor points on the boundary of the investigated structure. The fitness function is computed using an Artificial Neural Network (ANN).

The effect of the method of determination of Young's modulus on the estimation of fatigue life of structural elements

Abstract: Cyclic loading of a material entails modifications of its properties. In the paper, the problem of the influence of determination of the elasticity modulus $E$ on calculations of the fatigue life of structural elements was presented. Different values of the modulus of elasticity obtained by different methods were used for modelling of cyclic stress-strain curves and for analysis of local stresses and strains. In the calculations the strain-life and energy-life approach was applied.

Hierarchical genetic computation in optimal design

Abstract: The paper presents two examples of genetic hierarchic global optimization methods. They are two different goals of introducing hierarchy into the computational model: to perform the multi-scale search with the adapted accuracy and to better express the structure geometry in the optimal shape design. Results of the formal analysis and simple computational examples are also attached.

Application of the modified method of finite elements to identification of temperature of a body heated with a moving heat source

Abstract: A transient 2-dimensional problem of heat flow with a moving heat source is considered. It is assumed that the heat source is moving along one of the sides of a rectangle with a constant velocity. The unknown is the temperature distribution in a flat rectangular area. The paper presents an approximate solution which is based on the finite element method with a modified basis function. The space-time basis functions are combinations of heat polynomials which strictly satisfy the heat equation. Cartesian coordinates were used to solve the problem.

Hybrid, finite element-artificial neural network model for composite materials

Abstract: An application of Artificial Neural Networks for a definition of the effective constitutive law for a composite is described in the paper First, a classical homogenisation procedure is directly interpreted with a use of this numerical tool Next, a self-learning Finite Element code (FE with ANN inside) is used in the case when the effective constitutive law is deduced from a numerical experiment (substituting here a purely phenomenological approach) The new contribution to the classical self-learning procedure consists of its adaptation to a case of a non-monotonic loading (non one-to-one load-deformation curve) This new ability of the method is principally due to the incremental form of the constitutive equation and the respective scheme of the neural network structure Also an organisation of a constitutive data-base containing learning patterns is suitably modified It is shown by examples that the training process is very quick The error of this method is smaller, comparing to other schemes of data acquisition

On the problem of some interface defect filled with a compressible fluid in a periodic stratified medium

Abstract: Aperiodictwo-layeredelasticspacecontaininganinterfacedefectfilled withabarotropiccompressiblefluidisconsidered.Atinfinity,thecompositeissubjectedtoauniformlydistributedloadappliedperpendicularly tothelayering.Facesofthedefectareunderactionofconstantinternal fluid pressure.An approximatesolution to this problem is givenwithin acertainhomogenizedmodel.Theresultingsingularintegro-differential equationisobtainedandsolvedfortwotypesofdefectsbyusingananalogue of Dyson’s theorem. The influence of thefiller on the mechanical behaviouroftheconsideredbodyisanalysedandillustratedgraphically.

Vibration energy flow in rectangular plates

Abstract: The paper presents obtained from literature review formulas on structural intensity calculations The formulas involve loads (forces and moments) and strains (linear and angular) which enabled the estimation of structural surface intensity for beams, and plates considered here as simple structural elements The numerical method of intensity evaluation was based on complex modal analysis with the use of the finite element method The presented calculation results lead to the assessment of distribution of structural intensity vectors on the surface of a steel rectangular plate The models included the source of vibrations (force excitation) and sink of energy (damper) with known position of application The changes of the finite elements grid density enabled detailed investigation of the total vibration energy flow in the analysed plates

Numerical and experimental collapse analysis of tubular multi-member energy absorbers under lateral compression

Abstract: In the paper, the problem of collapse load and energy dissipation capacity of tubular multi-member energy absorbers subject to lateral crushing load is presented. The method of analytical solution of the problem of initial collapse load and load capacity at failure both for single-member and multi-member absorbers is discussed. A numerical Finite Element (FE) model of the multi-member absorber is presented and the parametric study of the influence of different absorber parameters (number of members, thickness of tubes, configuration of tubes) upon the collapse load and energy dissipation capacity is carried out. Results of numerical calculations are compared with those obtained from the experiment conducted by the authors. Both numerical and experimental results are presented in the form of load-deformation diagrams and diagrams of deformation patterns. Some final conclusions concerning the usefulness of multi-member tubular absorbers and indications into further investigations are derived.

Plane contact problems with partial slip for rough half-space

Abstract: Plane contact problems with the partial slip in the contact area are considered in the paper. To make the problems more realistic, the deformation of roughness of the contacting boundary is involved. The Shtayerman model of roughness is generalized on the case of tangential problems. The problems are treated by the boundary integral method. Examples of the contact of a flat rigid punch and a rigid cylinder with an elastic half-space involving boundary imperfections are studied. The effects of roughness parameters on the distribution of normal and shearing tractions as well as on the stick-slip transition are investigated.

Application of neurocomputing in the parametric identification using dynamic responses of structural elements – selected problems

Abstract: Some problems of neurocomputing in the dynamics of structures are presented: 1) damage detection using wave propagation, 2) updating of portal frames finite element models, 3) detection of the void and additional mass in cantilever plates, 4) neural network modelling of an ''artificial boundary condition''. The analysed problems are related to both data prepared by computational systems and that taken from experimental evidence.

Soft computing tools for machine diagnosing

Abstract: This work is aimed at creating soft computing tools for machine diagnosing systems. There are some problems with interpretating measured data in these systems. To overcome the problems with a big number of information in a diagnosing system, a neural pre-processor was proposed. A neural network can be used for reducing the size of analysed features. The fault detection and isolation is difficult due to context and broaden relations between measured data and a machine state. Soft computing methods are helpful in solving such problems. Artificial neural networks and fuzzy logic systems were used in these studies. An approximation of the unknown diagnostic relations symptom-state was done by both created tools. The only information about these relations were hidden in measured data that illustrate an expert knowledge formulated in a natural language. Such a form of information is the basis of constructing neural networks and fuzzy systems adequatly. The case study was fault detection of a high power fan. The working correctness of soft computing tools, presented in this work, was examined in the context of results obtained by utilisation of pattern recognition methods. The comparison of their performance speed, noise robustness and early detection of failure was also made.

Effect of changes in the thickness of a perforated plate of the heat exchanger on its structural stability

Abstract: One of the most important elements of heat exchangers are perforated bottoms These are perforated plates of significant thickness, in which heating cartridge pipes are mounted For the designers of heat exchangers, the strength analysis of the connection between the elements, which allows for the determination of the state of stress and calculation of displacements of the perforated bottom after fixing the pipes in it, is of special importance It results from carried out computations that the maximum reduced stresses in the perforated bottom are significantly lower than the values of admissible stresses In this paper, computations of stresses and strains for various thicknesses of the perforated bottom have been presented As a result of a decrease in the thickness of the perforated bottom, its deflection increases, and thus the heating system pipes are more exposed to strains and losses of stability

Random vortex method for three dimensional flows. Part I: Mathematical background

Abstract: The paper presents a mathematical formulation of the Lagrangian method suitable for numerical simulation of 3D viscous incompressible flows The vorticity field is approximated by a large ensemble of vortex particles which move with the fluid (advection) and perform random walks (diffusion) The charges of the particles change with time due to the stretching term in the governing equation The construction of the vortex particles ensures that the approximated vorticity field is strictly divergence-free at any time instant The boundary condition at the surface of an immersed body is satisfied by the creation of new vortex particles near the surface Various properties of induced velocity and vorticity fields are also discussed

Motion planning for wheeled mobile robot using potential field method

Abstract: A potential field method in the real-time approach toward avoidance of obstacles for a mobile robot has been developed. A collision-free path and goal-seeking behaviour are calculated using an artificial potential field method. The proposed reactive navigation approach is based on the coordination of elementary responses. To avoid convex obstacles, the navigator generates a ''reaching the middle of the collision-free space'' and goal-seeking behaviours. A control strategy based on artificial potential fields that generates a trajectory to be followed by a mobile robot that represents a reference for the robot at the same time is proposed. The effectiveness of the proposed method is numerically verified by a series of experiments on the emulator of the wheeled mobile robot Pioneer-2DX.

Cellular automata: structures and some applications

Abstract: A new approach to the modelling of various nature phenomena such as predator and prey ecological system, heat transport, spreading of oil slick and traffic flow is introduced. Cellular automata (CA) are discrete dynamical systems whose behaviour is completely specified in terms of simple local relations. They are mathematical models of spatially distributed processes; however they can lead to an appropriate simulation of complex dynamic processes. Applications to heat transfer and problems of environmental simulations are done. A discrete automaton model with fuzzy rules to simulate one-way traffic flow is also described. Results of simulations are consistent with phenomena observed in reality. It gives a base to propose the cellular automata tool as an option in modelling and solving problems of complex (and some times, not completely known) nature.

Computer simulation of catching of explosively propelling metal fragments by protective casing

Abstract: In the paper a mathematical-physical model, results of computer simulation of the propelling of metal fragments by pressure of detonation products and their catching by the protective casing made of a quasi-aramide fabric have been presented. The impact on the protective casing due to shock waves generated by the explosion has been examined. Depending on the nature of the issue, the 2D free particles or 1D Lagrange method has been used in the computer simulation.

A method of power distribution in the power transmission system of a remotely operated vehicle

Abstract: The paper addresses a method of distribution of propulsion for an unmanned underwater vehicle. The method is developed on basis of the decomposition of a configuration matrix describing the layout of thrusters in a power transmission system. The proposed solution of power distribution is worked out for the control system of the remotely operated vehicle ''Ukwial'' designed and built for the Polish Navy. The algorithm has been tested for track-keeping control both for faultless work of thrusters and failure of one of them. Some computer simulations are provided to demonstrate the effectiveness and correctness of the approach.