Recent progress in microelectronics and measurement techniques allows a growing number of critica... more Recent progress in microelectronics and measurement techniques allows a growing number of critical infrastructures to be equipped with Structural Health Monitoring (SHM) systems. Such SHM systems often consists of multiple measurement channels of different kinds of sensors, examples of which can be displacement transducers, strain gauges or accelerometers. Sensors in such systems should be placed in a proper way to facilitate extracting valuable information from the structure under investigation. In the case of relatively simple spatial truss structures, sensors can be located with the aid of the Effective Independence (EI) method proposed by Kammer [1]. However, in the case of large structures, which are intended to be equipped with hundreds if not thousands of sensors, other sensor placement methods may be needed. Recently, a promising idea of utilizing a topology optimization approach for the purpose of sensor placement has been proposed by Mariani et al. [2]. The goal of this st...
Third-order elastic coefficients (TOECs) have been measured experimentally and tabulated with pre... more Third-order elastic coefficients (TOECs) have been measured experimentally and tabulated with pretty good accuracy since the middle of the previous century. In the classical acoustic measurement method the recalculation of instantaneous stiffness change onto TOECs is based on the use of Green strain. In recent calculations performed by means of atomistic and quantum methods many different strain measures are employed. In result, quite different sets of TOECs can be obtained for the same material. In this paper, it is shown how dramatically the coefficients obtained depend on the choice of strain measure. The known formulas for calculation of the second derivative of a tensor-valued function of tensor variable are corrected. The formulas are essential for the correct analytic calculation of the tangent stiffness matrix in finite element method, among others.
EngOpt 2018 Proceedings of the 6th International Conference on Engineering Optimization, 2018
Optimal topologies obtained for structures subjected to deterministic loading can be sensitive to... more Optimal topologies obtained for structures subjected to deterministic loading can be sensitive to loading variations in terms of both magnitude and direction. Therefore, in this study we consider problem of topology optimization for structures subjected to probabilistic loading. The proposed method applies basic findings from probability theory, which allow to transform the original problem of topology optimization under single probabilistic loading into analogous problem of topology optimization under multiple deterministic loading cases. After recalling the theoretical background of the method,’ its effectiveness is demonstrated on an examples of cantilever structure subjected to horizontally oriented load with randomly varying angle of action.
The purpose of this study is to present an optimal design procedure for elasto-plastic structures... more The purpose of this study is to present an optimal design procedure for elasto-plastic structures subjected to impact loading. The proposed method is based on mode approximation of the displacement field and assumption of constant acceleration of impacted structure during whole time of deformation process until the plastic displacement limit is reached. Derivation of the method begins with the application of the principle of conservation of linear momentum, followed by determination of inertial forces. The final stage of the method utilizes an optimization technique in order to find a minimum weight structure. Eventually, effectiveness and usefulness of the proposed method is demonstrated on the example of a planar truss structure subjected to dynamic loading caused by a mass impacting the structure with a given initial velocity.
Bulletin of the Polish Academy of Sciences Technical Sciences, 2015
The main purpose of the study is an assessment of computational efficiency of selected numerical ... more The main purpose of the study is an assessment of computational efficiency of selected numerical methods for estimation of vibrational response statistics of a large multi-bearing turbo-generator rotor-shaft system. The effective estimation of the probability distribution of structural responses is essential for robust design optimization and reliability analysis of such systems. The analyzed scatter of responses is caused by random residual unbalances as well as random stiffness and damping parameters of the journal bearings. A proper representation of these uncertain parameters leads to multidimensional stochastic models. Three estimation techniques are compared: Monte Carlo sampling, Latin hypercube sampling and the sparse polynomial chaos expansion method. Based on the estimated values of the first four statistical moments the probability density function of the maximal vibration amplitude is evaluated by the maximal entropy principle method. The method is inherently suited for ...
The main objective of the presented study is an evaluation of the effectiveness of various method... more The main objective of the presented study is an evaluation of the effectiveness of various methods for estimating statistics of rotor-shaft vibration responses. The computational effectiveness as well as the accuracy of statistical moment estimation are essential for efficient robust design optimization of the rotor-shaft systems. The most important sources of the observed response scatter are inherently ran-dom rotor-shaft residual unbalances as well as stiffness and damping properties of the journal bearings. A relevant representation of these parameters leads to multidimensional stochastic models. The compared stochastic moment estimation methods include sampling techniques, the dimension reduction method and the polynomial chaos expansion method. Two problems of the rotor-shaft vibration analysis are considered: a typical single-span rotor-shaft of the 8-stage centrifugal compressor driven by the electric motor and a large multi-bearing rotor-shaft system of the steam turbogener...
Computer Assisted Mechanics and Engineering Sciences
One of the main obstacles in making stochastic simulation a standard design tool is its high comp... more One of the main obstacles in making stochastic simulation a standard design tool is its high computational cost. However, this problem can be significantly reduced by using efficient sampling techniques like optimal Latin hypercube (OLH) sampling. The paper advocates this kind of approach for scatter analysis of structural responses. After explaining the idea of the OLH sampling the principal component analysis method (PCA) is briefly described. Next, on numerical examples it is shown how this technique of statistical post-processing of simulation results can be used in the design process. Important improvements of the estimation quality offered by OLH design of experiments are illustrated on two numerical examples, one simple truss problem and one involving finite element analysis of elastic plate. Based on numerical experiments an attempt is made to propose the sample size which for a given number of random variables provides an acceptable estimation accuracy of statistical moment...
Recent progress in microelectronics and measurement techniques allows a growing number of critica... more Recent progress in microelectronics and measurement techniques allows a growing number of critical infrastructures to be equipped with Structural Health Monitoring (SHM) systems. Such SHM systems often consists of multiple measurement channels of different kinds of sensors, examples of which can be displacement transducers, strain gauges or accelerometers. Sensors in such systems should be placed in a proper way to facilitate extracting valuable information from the structure under investigation. In the case of relatively simple spatial truss structures, sensors can be located with the aid of the Effective Independence (EI) method proposed by Kammer [1]. However, in the case of large structures, which are intended to be equipped with hundreds if not thousands of sensors, other sensor placement methods may be needed. Recently, a promising idea of utilizing a topology optimization approach for the purpose of sensor placement has been proposed by Mariani et al. [2]. The goal of this st...
Third-order elastic coefficients (TOECs) have been measured experimentally and tabulated with pre... more Third-order elastic coefficients (TOECs) have been measured experimentally and tabulated with pretty good accuracy since the middle of the previous century. In the classical acoustic measurement method the recalculation of instantaneous stiffness change onto TOECs is based on the use of Green strain. In recent calculations performed by means of atomistic and quantum methods many different strain measures are employed. In result, quite different sets of TOECs can be obtained for the same material. In this paper, it is shown how dramatically the coefficients obtained depend on the choice of strain measure. The known formulas for calculation of the second derivative of a tensor-valued function of tensor variable are corrected. The formulas are essential for the correct analytic calculation of the tangent stiffness matrix in finite element method, among others.
EngOpt 2018 Proceedings of the 6th International Conference on Engineering Optimization, 2018
Optimal topologies obtained for structures subjected to deterministic loading can be sensitive to... more Optimal topologies obtained for structures subjected to deterministic loading can be sensitive to loading variations in terms of both magnitude and direction. Therefore, in this study we consider problem of topology optimization for structures subjected to probabilistic loading. The proposed method applies basic findings from probability theory, which allow to transform the original problem of topology optimization under single probabilistic loading into analogous problem of topology optimization under multiple deterministic loading cases. After recalling the theoretical background of the method,’ its effectiveness is demonstrated on an examples of cantilever structure subjected to horizontally oriented load with randomly varying angle of action.
The purpose of this study is to present an optimal design procedure for elasto-plastic structures... more The purpose of this study is to present an optimal design procedure for elasto-plastic structures subjected to impact loading. The proposed method is based on mode approximation of the displacement field and assumption of constant acceleration of impacted structure during whole time of deformation process until the plastic displacement limit is reached. Derivation of the method begins with the application of the principle of conservation of linear momentum, followed by determination of inertial forces. The final stage of the method utilizes an optimization technique in order to find a minimum weight structure. Eventually, effectiveness and usefulness of the proposed method is demonstrated on the example of a planar truss structure subjected to dynamic loading caused by a mass impacting the structure with a given initial velocity.
Bulletin of the Polish Academy of Sciences Technical Sciences, 2015
The main purpose of the study is an assessment of computational efficiency of selected numerical ... more The main purpose of the study is an assessment of computational efficiency of selected numerical methods for estimation of vibrational response statistics of a large multi-bearing turbo-generator rotor-shaft system. The effective estimation of the probability distribution of structural responses is essential for robust design optimization and reliability analysis of such systems. The analyzed scatter of responses is caused by random residual unbalances as well as random stiffness and damping parameters of the journal bearings. A proper representation of these uncertain parameters leads to multidimensional stochastic models. Three estimation techniques are compared: Monte Carlo sampling, Latin hypercube sampling and the sparse polynomial chaos expansion method. Based on the estimated values of the first four statistical moments the probability density function of the maximal vibration amplitude is evaluated by the maximal entropy principle method. The method is inherently suited for ...
The main objective of the presented study is an evaluation of the effectiveness of various method... more The main objective of the presented study is an evaluation of the effectiveness of various methods for estimating statistics of rotor-shaft vibration responses. The computational effectiveness as well as the accuracy of statistical moment estimation are essential for efficient robust design optimization of the rotor-shaft systems. The most important sources of the observed response scatter are inherently ran-dom rotor-shaft residual unbalances as well as stiffness and damping properties of the journal bearings. A relevant representation of these parameters leads to multidimensional stochastic models. The compared stochastic moment estimation methods include sampling techniques, the dimension reduction method and the polynomial chaos expansion method. Two problems of the rotor-shaft vibration analysis are considered: a typical single-span rotor-shaft of the 8-stage centrifugal compressor driven by the electric motor and a large multi-bearing rotor-shaft system of the steam turbogener...
Computer Assisted Mechanics and Engineering Sciences
One of the main obstacles in making stochastic simulation a standard design tool is its high comp... more One of the main obstacles in making stochastic simulation a standard design tool is its high computational cost. However, this problem can be significantly reduced by using efficient sampling techniques like optimal Latin hypercube (OLH) sampling. The paper advocates this kind of approach for scatter analysis of structural responses. After explaining the idea of the OLH sampling the principal component analysis method (PCA) is briefly described. Next, on numerical examples it is shown how this technique of statistical post-processing of simulation results can be used in the design process. Important improvements of the estimation quality offered by OLH design of experiments are illustrated on two numerical examples, one simple truss problem and one involving finite element analysis of elastic plate. Based on numerical experiments an attempt is made to propose the sample size which for a given number of random variables provides an acceptable estimation accuracy of statistical moment...
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Papers by Piotr Tauzowski