Urszula Radoń - Academia.edu (original) (raw)

Papers by Urszula Radoń

Research paper thumbnail of Robust Optimization of the Steel Single Story Frame

Acta Polytechnica Hungarica

In contemporary design practices, building structures are expected to not only meet safety requir... more In contemporary design practices, building structures are expected to not only meet safety requirements but also be optimized. However, optimal designs can be highly sensitive to random variations in model parameters and external actions. Solutions that appear effective under nominal conditions may prove inadequate when parameter randomness is considered. To address this challenge, the concept of robust optimization has been introduced, which extends deterministic optimization formulations to incorporate the random variability of parameter values. In this study, we demonstrate the applicability of robust optimization in the design of building structures using a simple orthogonal frame as an example. The static-strength analysis is conducted based on the displacement method, utilizing second-order theory. To assess the safety level of the steel frame, a preliminary evaluation is performed by determining the reliability index and failure probability using the Monte Carlo Method. Robust optimization is then employed, leveraging the second-order response surface. Experimental designs are generated following an optimal Latin hypercube plan. The proposal of a mathematical-numerical algorithm for solving the optimization problem while considering the random nature of design parameters constitutes the innovative aspect of this research.

Research paper thumbnail of Dynamic Analysis of a Steel-Concrete Railway Bridges of Langer Type Under the Influence of a Moving Load

Structure and Environment

The studying the dynamic response of steel-concrete railway bridges of Langer type is huge import... more The studying the dynamic response of steel-concrete railway bridges of Langer type is huge importance of ensuring the safety of such structures under high-speed train loads. Numerical simulations at the design stage require knowledge of the modal characteristics: natural frequencies, shapes and damping. In addition, in the dynamics of railway bridges subjected to high-speed trains, it is important to check the impact of dynamic effects on the ultimate and serviceability limit states. As part of the investigations displacements and accelerations of selected measurement points arising from driving the test rolling stock are analyzed. In the first stage, calculations of the eigenvalues and the corresponding eigenvectors were carried out in the Robot program for two variants of mass description (distributed and discrete). In the second stage, dynamic train passages for various vehicle speeds were examined in terms of displacements and accelerations of measurement points by using the aut...

Research paper thumbnail of The reliability assessment for steel industrial building

Research paper thumbnail of Definicja modelu matematycznego w ocenie niezawodności konstrukcji prętowych

Celem pracy jest analiza statyczna konstrukcji nośnej hali stalowej w ujeciu probabilistycznym. Z... more Celem pracy jest analiza statyczna konstrukcji nośnej hali stalowej w ujeciu probabilistycznym. Zaproponowano ilościowe, w porownaniu z normą Eurokod 0, określenie niezawodności konstrukcji. Parametry projektowe konstrukcji zdefiniowano jako wielkości deterministyczne oraz zmienne losowe. Zmienne losowe nie są skorelowane. Kryterium awarii konstrukcji określają funkcje graniczne związane ze stanem granicznym nośności i uzytkowalności. W opisie stanow granicznych konstrukcji zdefiniowano jawne funkcje graniczne wygenerowe w programie Mathematica. W analizie niezawodności posluzono sie programem niezawodnościowym STAND. Wyznaczono wskaźnik niezawodności Hasofera-Linda. Podstawową metodą badawczą jest metoda FORM. W celu weryfikacji poprawności obliczen zastosowano metody: SORM, Monte Carlo oraz Importance Sampling. W opisie zmiennych losowych wykorzystano rozne typy rozkladu prawdopodobienstwa i porownano wartości wskaźnika przy rozkladzie normalnym oraz przy dobraniu najbardziej adekwatnego rozkladu do rodzaju zmiennej. Wyznaczono wrazliwośc wskaźnika niezawodności na zmienne losowe. Jezeli wrazliwośc wskaźnika niezawodności ze wzgledu na zmienną losową X jest mala w porownaniu do innych zmiennych to mozemy uznac, iz wplyw tej zmiennej na wartośc prawdopodobienstwa awarii jest niewielki i w kolejnych obliczeniach traktowac ją jako parametr deterministyczny. Analiza wrazliwości prowadzi wiec do uproszczenia opisu modelu matematycznego i ponownego wyznaczenia funkcji granicznej oraz wskaźnika niezawodności Hasofera-Linda. W przedstawionych przykladach analizy niezawodności wykorzystano program STAND.

Research paper thumbnail of Analiza niezawodności konstrukcji kratowej

Acta Scientiarum Polonorum. Architectura, 2009

Research paper thumbnail of Effect of Increased Density of Nodes in Geodesic Dome on its Critical Load Capacity

IOP conference series, Feb 23, 2019

The paper reports an attempt at assessing the effect of geodesic dome mesh refinement on the stru... more The paper reports an attempt at assessing the effect of geodesic dome mesh refinement on the structure critical load capacity. The initial surface of geodesic domes is the sphere divided into spherical triangles. Consecutive divisions of the spherical triangles decide the mesh refinement of the geodesic domes. Two computational models (3V and 4V) were examined. For 4V dome, two types of structure, namely truss and frame ones were considered. For 4V frame system, the values of the critical load capacity were determined for three buckling lengths of the bars μ: 0.5, 0.7 and 1.0.

Research paper thumbnail of The influence of boundary conditions on the safety of steel trusses subjected to high temperatures

Structure and Environment, 2017

Research paper thumbnail of Analysis of Reliability and Stability of Bar Structures / Analiza Niezawodnosci I Statecznosci Konstrukcji Pretowej

Archives of civil engineering, Jun 1, 2010

In the paper, the Hasofer-Lind index is applied for determining the probability of stability loss... more In the paper, the Hasofer-Lind index is applied for determining the probability of stability loss of truss structure under random load. In 1974 Hasofer-Lind proposed a modified reliability index that did not exhibit the invariance problem. The "correction" is the evaluation the limit state function at a point known as the "design point", instead of the mean values. The design point is generally not known a priori, an iteration technique must be used to find out the reliability index. The paper shows how the reliability index changes under the influence of different variables mean value, standard deviation, and probability density function.

Research paper thumbnail of Reliability analysis of Misses truss

Archives of Civil and Mechanical Engineering, 2011

The present study considers the problems of stability and reliability of truss structure suscepti... more The present study considers the problems of stability and reliability of truss structure susceptible to stability loss from the condition of node snapping. In the reliability analysis of structure, uncertain parameters, such us load magnitudes, the axial stiffness of bars, coordinate nodes are represented by random variables. Random variables are not correlated. The criterion of structural failure is expressed by the condition of non-exceeding the admissible load multiplier. In the current paper only the time independent component reliability analysis problems are considered. The Hasofer-Lind index in conjunction with transformation method in the FORM was used as a reliability measure.

Research paper thumbnail of Proposal for the Assessment of Steel Truss Reliability Under Fire Conditions

Archives of civil engineering, Dec 1, 2015

The paper presents a proposal for the assessment of the reliability of steel truss (both statical... more The paper presents a proposal for the assessment of the reliability of steel truss (both statically determinate and indeterminate) in the persistent and accidental design situation. In the analysis, a probabilistic approach was used. The global Hasofer-Lind reliability index was employed, computed in successive time steps for the whole structure, not for individual elements. The statically determinate truss was modelled as a serial system from the reliability standpoint. For the statically indeterminate truss, kinematically admissible failure mechanisms were determined by means of the examination of the singularity of the stiffness matrix of the structure, converting the truss into a geometrically variable system. For the problem thus formulated, a serial-parallel reliability model was constructed. Monitoring the reliability index in the successive minutes of the fire makes it possible to estimate the probability of the structure failure, and to decide whether the required safety level is maintained.

Research paper thumbnail of Effects of single-layer truss dome geometry on critical load capacity

Structure and Environment, 2017

The purpose of this article is to estimate the effect of geometric imperfections on critical load... more The purpose of this article is to estimate the effect of geometric imperfections on critical loads. Special attention was paid to trusses subjected to large displacement gradients and vulnerable to stability loss due to snapping. The article uses the Lagrangian description for geometric nonlinearities. The truss stability analysis was performed using the Finite Element Method. The equilibrium path was determined using the scalar current parameter of stiffness and method of arc length constant.

Research paper thumbnail of The Evaluation Of Algorithms For Determination Of The Reliability Index

Archives of civil engineering, Sep 1, 2015

The study deals with stability and dynamic problems in bar structures using a probabilistic appro... more The study deals with stability and dynamic problems in bar structures using a probabilistic approach. Structural design parameters are defined as deterministic values and also as random variables, which are not correlated. The criterion of structural failure is expressed by the condition of non-exceeding the admissible load multiplier and condition of non-exceeding the admissible vertical displacement. The Hasofer-Lind index was used as a reliability measure. The primary research tool is the FORM method. In order to verify the correctness of the calculations Monte Carlo and Importance Sampling methods were used. The sensitivity of the reliability index to the random variables was defined. The limit state function is not an explicit function of random variables. This dependence was determined using a numerical procedure, e.g. the finite element methods. The paper aims to present the communication between the STAND reliability analysis program and the KRATA and MES3D external FE programs.

Research paper thumbnail of The Influence of Dome Geometry on the Results of Modal and Buckling Analysis

Applied sciences, Feb 20, 2023

This article is an open access article distributed under the terms and conditions of the Creative... more This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY

Research paper thumbnail of Robust optimisation of a single-layer lattice dome

Modern Trends in Research on Steel, Aluminium and Composite Structures, 2021

The formulation of deterministic optimization in no way takes into account the randomness of the ... more The formulation of deterministic optimization in no way takes into account the randomness of the design variables [Chybiński, M., Garstecki, A. (2017), Czubacki, R., Lewiński T. (2020)]. Optimum structures are particularly sensitive to parameter imperfections. Optimal solutions located on the border of the acceptable area may relatively easily turn out to be completely useless if the parameter values differ from the assumed nominal values. It seems natural to extend the formulation of deterministic optimization, which takes into account the uncertainty of parameter values. Robust optimization proposed in the paper offers such possibilities. In the paper, robust optimisation is discussed on the example of a single-layer lattice covering. After dimensioning the individual groups of bars, the safety level of the structure was assessed by determining the reliability index and failure probability. The structure under analysis is susceptible to stability failure resulting from the condition of the node snap-through. On this basis, a displacement limit function was adopted, which refers to the maximum displacement value at the instant of the node snap-through. Next, two methods of structure optimisation (deterministic and robust), based on analogous constraints and objective function, were compared. The comparison of both methods ends with a reassessment of the safety level of the structure. As a result of robust optimization, a structure with a slightly larger mass was obtained. The difference in the weight of the struc ture in the case of deterministic and immunity optimization did not exceed 2%. However, the reliability index, which measures the safety of the structure, has increased significantly. At the expense of a slight increase in weight, we obtained a structure that is more reliable and resist ant to the dispersion of parameters characterizing the structure's operation.

Research paper thumbnail of Zastosowanie metody FORM w analizie niezawodności konstrukcji kratowych podatnych na przeskok (Application method FORM in reliability analysis of node snapping truss structures)

Wydawnictwo Politechniki Świętokrzyskiej, 2012

Research paper thumbnail of Comparison of the Reliability Methods for Steel Trusses Subjected to Fire

IOP Conference Series: Materials Science and Engineering, 2017

Research paper thumbnail of Reliability analysis of the supporting structure subjected to the action forced vibrations

Structure and Environment, 2015

The study concerns the forced vibrations analysis of supporting structure in terms of probabilism... more The study concerns the forced vibrations analysis of supporting structure in terms of probabilism. Structural design parameters are defined as the deterministic values and random variables. Random variables are not correlated. The criterion for structural failure is expressed as the limit of functions referring to the ultimate and serviceability limit state. The condition takes into account the material fatigue. The Hasofer-Lind reliability index and the probability of failure was determined. In calculations of reliability methods were used: FORM, SORM, Monte Carlo and Importance Sampling methods. The STAND program is used to present the examples of reliability analysis.

Research paper thumbnail of Effects of single-layer truss dome geometry on critical load capacity

Structure and Environment, 2017

S t r e s z c z e n i e Celem artykułu jest oszacowanie wpływu imperfekcji geometrycznych na obci... more S t r e s z c z e n i e Celem artykułu jest oszacowanie wpływu imperfekcji geometrycznych na obciążenie krytyczne. Szczególną uwagę zwrócono na kratownice poddane dużym gradientom przemieszczeń i podatne na utratę stateczności przez przeskok. W pracy zastosowano opis Lagrange’a uwzględniający nieliniowości geometryczne. Analizę stateczności kratownicy przeprowadzano za pomocą metody elementów skończonych. Do określenia ścieżki równowagi wykorzystano metodę skalarnego parametru sztywności i metodę stałej długości łuku. Słowa kluczowe: stateczność, analiza nieliniowa, ścieżka równowagi, imperfekcje geometryczne, obciążenie krytyczne WOJCIECH MOCHOCKI PAULINA OBARA URSZULA RADOŃ PAWEŁ ZABOJSZCZA Kielce University of Technology e-mail: wmochocki@tu.kielce.pl e-mail: paula@tu.kielce.pl e-mail: zmbur@tu.kielce.pl e-mail: p.zabojszcza@student.tu.kielce.pl EFFECTS OF SINGLE-LAYER TRUSS DOME GEOMETRY ON CRITICAL LOAD CAPACITY WPŁYW ZMIAN GEOMETRII NA NOŚNOŚĆ KRYTYCZNĄ JEDNOWARSTWOWEJ KOPUŁY ...

Research paper thumbnail of Definicja modelu matematycznego w ocenie niezawodności konstrukcji prętowych

Celem pracy jest analiza statyczna konstrukcji nośnej hali stalowej w ujeciu probabilistycznym. Z... more Celem pracy jest analiza statyczna konstrukcji nośnej hali stalowej w ujeciu probabilistycznym. Zaproponowano ilościowe, w porownaniu z normą Eurokod 0, określenie niezawodności konstrukcji. Parametry projektowe konstrukcji zdefiniowano jako wielkości deterministyczne oraz zmienne losowe. Zmienne losowe nie są skorelowane. Kryterium awarii konstrukcji określają funkcje graniczne związane ze stanem granicznym nośności i uzytkowalności. W opisie stanow granicznych konstrukcji zdefiniowano jawne funkcje graniczne wygenerowe w programie Mathematica. W analizie niezawodności posluzono sie programem niezawodnościowym STAND. Wyznaczono wskaźnik niezawodności Hasofera-Linda. Podstawową metodą badawczą jest metoda FORM. W celu weryfikacji poprawności obliczen zastosowano metody: SORM, Monte Carlo oraz Importance Sampling. W opisie zmiennych losowych wykorzystano rozne typy rozkladu prawdopodobienstwa i porownano wartości wskaźnika przy rozkladzie normalnym oraz przy dobraniu najbardziej adek...

Research paper thumbnail of Structure Stability Under Multiparameter Loads

Engineering Transactions, 1999

The precritical response analysis of a structure is generally sufficient for designing purposes. ... more The precritical response analysis of a structure is generally sufficient for designing purposes. However, the prediction of the response in the postcritical range is essential to identify the ability of the structure to sustain loads at large values of displacements. The modern stability analysis usually consists in generating the equilibrium path for a structure and determining its critical points, but this way is admissible only for one-parameter loads. The formal procedure allows to continue the above procedure for the multiparameter systems, although, equilibrium path should be converted into equilibrium surface or hypersurface. It must clearly be said that this method is useless for the practice due to its complexity. In the paper, the proposal of solving this problem and determining the probability of stability loss is presented.

Research paper thumbnail of Robust Optimization of the Steel Single Story Frame

Acta Polytechnica Hungarica

In contemporary design practices, building structures are expected to not only meet safety requir... more In contemporary design practices, building structures are expected to not only meet safety requirements but also be optimized. However, optimal designs can be highly sensitive to random variations in model parameters and external actions. Solutions that appear effective under nominal conditions may prove inadequate when parameter randomness is considered. To address this challenge, the concept of robust optimization has been introduced, which extends deterministic optimization formulations to incorporate the random variability of parameter values. In this study, we demonstrate the applicability of robust optimization in the design of building structures using a simple orthogonal frame as an example. The static-strength analysis is conducted based on the displacement method, utilizing second-order theory. To assess the safety level of the steel frame, a preliminary evaluation is performed by determining the reliability index and failure probability using the Monte Carlo Method. Robust optimization is then employed, leveraging the second-order response surface. Experimental designs are generated following an optimal Latin hypercube plan. The proposal of a mathematical-numerical algorithm for solving the optimization problem while considering the random nature of design parameters constitutes the innovative aspect of this research.

Research paper thumbnail of Dynamic Analysis of a Steel-Concrete Railway Bridges of Langer Type Under the Influence of a Moving Load

Structure and Environment

The studying the dynamic response of steel-concrete railway bridges of Langer type is huge import... more The studying the dynamic response of steel-concrete railway bridges of Langer type is huge importance of ensuring the safety of such structures under high-speed train loads. Numerical simulations at the design stage require knowledge of the modal characteristics: natural frequencies, shapes and damping. In addition, in the dynamics of railway bridges subjected to high-speed trains, it is important to check the impact of dynamic effects on the ultimate and serviceability limit states. As part of the investigations displacements and accelerations of selected measurement points arising from driving the test rolling stock are analyzed. In the first stage, calculations of the eigenvalues and the corresponding eigenvectors were carried out in the Robot program for two variants of mass description (distributed and discrete). In the second stage, dynamic train passages for various vehicle speeds were examined in terms of displacements and accelerations of measurement points by using the aut...

Research paper thumbnail of The reliability assessment for steel industrial building

Research paper thumbnail of Definicja modelu matematycznego w ocenie niezawodności konstrukcji prętowych

Celem pracy jest analiza statyczna konstrukcji nośnej hali stalowej w ujeciu probabilistycznym. Z... more Celem pracy jest analiza statyczna konstrukcji nośnej hali stalowej w ujeciu probabilistycznym. Zaproponowano ilościowe, w porownaniu z normą Eurokod 0, określenie niezawodności konstrukcji. Parametry projektowe konstrukcji zdefiniowano jako wielkości deterministyczne oraz zmienne losowe. Zmienne losowe nie są skorelowane. Kryterium awarii konstrukcji określają funkcje graniczne związane ze stanem granicznym nośności i uzytkowalności. W opisie stanow granicznych konstrukcji zdefiniowano jawne funkcje graniczne wygenerowe w programie Mathematica. W analizie niezawodności posluzono sie programem niezawodnościowym STAND. Wyznaczono wskaźnik niezawodności Hasofera-Linda. Podstawową metodą badawczą jest metoda FORM. W celu weryfikacji poprawności obliczen zastosowano metody: SORM, Monte Carlo oraz Importance Sampling. W opisie zmiennych losowych wykorzystano rozne typy rozkladu prawdopodobienstwa i porownano wartości wskaźnika przy rozkladzie normalnym oraz przy dobraniu najbardziej adekwatnego rozkladu do rodzaju zmiennej. Wyznaczono wrazliwośc wskaźnika niezawodności na zmienne losowe. Jezeli wrazliwośc wskaźnika niezawodności ze wzgledu na zmienną losową X jest mala w porownaniu do innych zmiennych to mozemy uznac, iz wplyw tej zmiennej na wartośc prawdopodobienstwa awarii jest niewielki i w kolejnych obliczeniach traktowac ją jako parametr deterministyczny. Analiza wrazliwości prowadzi wiec do uproszczenia opisu modelu matematycznego i ponownego wyznaczenia funkcji granicznej oraz wskaźnika niezawodności Hasofera-Linda. W przedstawionych przykladach analizy niezawodności wykorzystano program STAND.

Research paper thumbnail of Analiza niezawodności konstrukcji kratowej

Acta Scientiarum Polonorum. Architectura, 2009

Research paper thumbnail of Effect of Increased Density of Nodes in Geodesic Dome on its Critical Load Capacity

IOP conference series, Feb 23, 2019

The paper reports an attempt at assessing the effect of geodesic dome mesh refinement on the stru... more The paper reports an attempt at assessing the effect of geodesic dome mesh refinement on the structure critical load capacity. The initial surface of geodesic domes is the sphere divided into spherical triangles. Consecutive divisions of the spherical triangles decide the mesh refinement of the geodesic domes. Two computational models (3V and 4V) were examined. For 4V dome, two types of structure, namely truss and frame ones were considered. For 4V frame system, the values of the critical load capacity were determined for three buckling lengths of the bars μ: 0.5, 0.7 and 1.0.

Research paper thumbnail of The influence of boundary conditions on the safety of steel trusses subjected to high temperatures

Structure and Environment, 2017

Research paper thumbnail of Analysis of Reliability and Stability of Bar Structures / Analiza Niezawodnosci I Statecznosci Konstrukcji Pretowej

Archives of civil engineering, Jun 1, 2010

In the paper, the Hasofer-Lind index is applied for determining the probability of stability loss... more In the paper, the Hasofer-Lind index is applied for determining the probability of stability loss of truss structure under random load. In 1974 Hasofer-Lind proposed a modified reliability index that did not exhibit the invariance problem. The "correction" is the evaluation the limit state function at a point known as the "design point", instead of the mean values. The design point is generally not known a priori, an iteration technique must be used to find out the reliability index. The paper shows how the reliability index changes under the influence of different variables mean value, standard deviation, and probability density function.

Research paper thumbnail of Reliability analysis of Misses truss

Archives of Civil and Mechanical Engineering, 2011

The present study considers the problems of stability and reliability of truss structure suscepti... more The present study considers the problems of stability and reliability of truss structure susceptible to stability loss from the condition of node snapping. In the reliability analysis of structure, uncertain parameters, such us load magnitudes, the axial stiffness of bars, coordinate nodes are represented by random variables. Random variables are not correlated. The criterion of structural failure is expressed by the condition of non-exceeding the admissible load multiplier. In the current paper only the time independent component reliability analysis problems are considered. The Hasofer-Lind index in conjunction with transformation method in the FORM was used as a reliability measure.

Research paper thumbnail of Proposal for the Assessment of Steel Truss Reliability Under Fire Conditions

Archives of civil engineering, Dec 1, 2015

The paper presents a proposal for the assessment of the reliability of steel truss (both statical... more The paper presents a proposal for the assessment of the reliability of steel truss (both statically determinate and indeterminate) in the persistent and accidental design situation. In the analysis, a probabilistic approach was used. The global Hasofer-Lind reliability index was employed, computed in successive time steps for the whole structure, not for individual elements. The statically determinate truss was modelled as a serial system from the reliability standpoint. For the statically indeterminate truss, kinematically admissible failure mechanisms were determined by means of the examination of the singularity of the stiffness matrix of the structure, converting the truss into a geometrically variable system. For the problem thus formulated, a serial-parallel reliability model was constructed. Monitoring the reliability index in the successive minutes of the fire makes it possible to estimate the probability of the structure failure, and to decide whether the required safety level is maintained.

Research paper thumbnail of Effects of single-layer truss dome geometry on critical load capacity

Structure and Environment, 2017

The purpose of this article is to estimate the effect of geometric imperfections on critical load... more The purpose of this article is to estimate the effect of geometric imperfections on critical loads. Special attention was paid to trusses subjected to large displacement gradients and vulnerable to stability loss due to snapping. The article uses the Lagrangian description for geometric nonlinearities. The truss stability analysis was performed using the Finite Element Method. The equilibrium path was determined using the scalar current parameter of stiffness and method of arc length constant.

Research paper thumbnail of The Evaluation Of Algorithms For Determination Of The Reliability Index

Archives of civil engineering, Sep 1, 2015

The study deals with stability and dynamic problems in bar structures using a probabilistic appro... more The study deals with stability and dynamic problems in bar structures using a probabilistic approach. Structural design parameters are defined as deterministic values and also as random variables, which are not correlated. The criterion of structural failure is expressed by the condition of non-exceeding the admissible load multiplier and condition of non-exceeding the admissible vertical displacement. The Hasofer-Lind index was used as a reliability measure. The primary research tool is the FORM method. In order to verify the correctness of the calculations Monte Carlo and Importance Sampling methods were used. The sensitivity of the reliability index to the random variables was defined. The limit state function is not an explicit function of random variables. This dependence was determined using a numerical procedure, e.g. the finite element methods. The paper aims to present the communication between the STAND reliability analysis program and the KRATA and MES3D external FE programs.

Research paper thumbnail of The Influence of Dome Geometry on the Results of Modal and Buckling Analysis

Applied sciences, Feb 20, 2023

This article is an open access article distributed under the terms and conditions of the Creative... more This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY

Research paper thumbnail of Robust optimisation of a single-layer lattice dome

Modern Trends in Research on Steel, Aluminium and Composite Structures, 2021

The formulation of deterministic optimization in no way takes into account the randomness of the ... more The formulation of deterministic optimization in no way takes into account the randomness of the design variables [Chybiński, M., Garstecki, A. (2017), Czubacki, R., Lewiński T. (2020)]. Optimum structures are particularly sensitive to parameter imperfections. Optimal solutions located on the border of the acceptable area may relatively easily turn out to be completely useless if the parameter values differ from the assumed nominal values. It seems natural to extend the formulation of deterministic optimization, which takes into account the uncertainty of parameter values. Robust optimization proposed in the paper offers such possibilities. In the paper, robust optimisation is discussed on the example of a single-layer lattice covering. After dimensioning the individual groups of bars, the safety level of the structure was assessed by determining the reliability index and failure probability. The structure under analysis is susceptible to stability failure resulting from the condition of the node snap-through. On this basis, a displacement limit function was adopted, which refers to the maximum displacement value at the instant of the node snap-through. Next, two methods of structure optimisation (deterministic and robust), based on analogous constraints and objective function, were compared. The comparison of both methods ends with a reassessment of the safety level of the structure. As a result of robust optimization, a structure with a slightly larger mass was obtained. The difference in the weight of the struc ture in the case of deterministic and immunity optimization did not exceed 2%. However, the reliability index, which measures the safety of the structure, has increased significantly. At the expense of a slight increase in weight, we obtained a structure that is more reliable and resist ant to the dispersion of parameters characterizing the structure's operation.

Research paper thumbnail of Zastosowanie metody FORM w analizie niezawodności konstrukcji kratowych podatnych na przeskok (Application method FORM in reliability analysis of node snapping truss structures)

Wydawnictwo Politechniki Świętokrzyskiej, 2012

Research paper thumbnail of Comparison of the Reliability Methods for Steel Trusses Subjected to Fire

IOP Conference Series: Materials Science and Engineering, 2017

Research paper thumbnail of Reliability analysis of the supporting structure subjected to the action forced vibrations

Structure and Environment, 2015

The study concerns the forced vibrations analysis of supporting structure in terms of probabilism... more The study concerns the forced vibrations analysis of supporting structure in terms of probabilism. Structural design parameters are defined as the deterministic values and random variables. Random variables are not correlated. The criterion for structural failure is expressed as the limit of functions referring to the ultimate and serviceability limit state. The condition takes into account the material fatigue. The Hasofer-Lind reliability index and the probability of failure was determined. In calculations of reliability methods were used: FORM, SORM, Monte Carlo and Importance Sampling methods. The STAND program is used to present the examples of reliability analysis.

Research paper thumbnail of Effects of single-layer truss dome geometry on critical load capacity

Structure and Environment, 2017

S t r e s z c z e n i e Celem artykułu jest oszacowanie wpływu imperfekcji geometrycznych na obci... more S t r e s z c z e n i e Celem artykułu jest oszacowanie wpływu imperfekcji geometrycznych na obciążenie krytyczne. Szczególną uwagę zwrócono na kratownice poddane dużym gradientom przemieszczeń i podatne na utratę stateczności przez przeskok. W pracy zastosowano opis Lagrange’a uwzględniający nieliniowości geometryczne. Analizę stateczności kratownicy przeprowadzano za pomocą metody elementów skończonych. Do określenia ścieżki równowagi wykorzystano metodę skalarnego parametru sztywności i metodę stałej długości łuku. Słowa kluczowe: stateczność, analiza nieliniowa, ścieżka równowagi, imperfekcje geometryczne, obciążenie krytyczne WOJCIECH MOCHOCKI PAULINA OBARA URSZULA RADOŃ PAWEŁ ZABOJSZCZA Kielce University of Technology e-mail: wmochocki@tu.kielce.pl e-mail: paula@tu.kielce.pl e-mail: zmbur@tu.kielce.pl e-mail: p.zabojszcza@student.tu.kielce.pl EFFECTS OF SINGLE-LAYER TRUSS DOME GEOMETRY ON CRITICAL LOAD CAPACITY WPŁYW ZMIAN GEOMETRII NA NOŚNOŚĆ KRYTYCZNĄ JEDNOWARSTWOWEJ KOPUŁY ...

Research paper thumbnail of Definicja modelu matematycznego w ocenie niezawodności konstrukcji prętowych

Celem pracy jest analiza statyczna konstrukcji nośnej hali stalowej w ujeciu probabilistycznym. Z... more Celem pracy jest analiza statyczna konstrukcji nośnej hali stalowej w ujeciu probabilistycznym. Zaproponowano ilościowe, w porownaniu z normą Eurokod 0, określenie niezawodności konstrukcji. Parametry projektowe konstrukcji zdefiniowano jako wielkości deterministyczne oraz zmienne losowe. Zmienne losowe nie są skorelowane. Kryterium awarii konstrukcji określają funkcje graniczne związane ze stanem granicznym nośności i uzytkowalności. W opisie stanow granicznych konstrukcji zdefiniowano jawne funkcje graniczne wygenerowe w programie Mathematica. W analizie niezawodności posluzono sie programem niezawodnościowym STAND. Wyznaczono wskaźnik niezawodności Hasofera-Linda. Podstawową metodą badawczą jest metoda FORM. W celu weryfikacji poprawności obliczen zastosowano metody: SORM, Monte Carlo oraz Importance Sampling. W opisie zmiennych losowych wykorzystano rozne typy rozkladu prawdopodobienstwa i porownano wartości wskaźnika przy rozkladzie normalnym oraz przy dobraniu najbardziej adek...

Research paper thumbnail of Structure Stability Under Multiparameter Loads

Engineering Transactions, 1999

The precritical response analysis of a structure is generally sufficient for designing purposes. ... more The precritical response analysis of a structure is generally sufficient for designing purposes. However, the prediction of the response in the postcritical range is essential to identify the ability of the structure to sustain loads at large values of displacements. The modern stability analysis usually consists in generating the equilibrium path for a structure and determining its critical points, but this way is admissible only for one-parameter loads. The formal procedure allows to continue the above procedure for the multiparameter systems, although, equilibrium path should be converted into equilibrium surface or hypersurface. It must clearly be said that this method is useless for the practice due to its complexity. In the paper, the proposal of solving this problem and determining the probability of stability loss is presented.