Papers by Elias Paraskevopoulos
Bulletin of Earthquake Engineering, 2022
Bridges are the most critical and usually the most vulnerable structural component of a road netw... more Bridges are the most critical and usually the most vulnerable structural component of a road network exposed to various hazards. Damage due to recent earthquakes worldwide highlighted the substantial direct and indirect financial losses related to partial or total collapse of critical bridge components and pointed to the need for reliable assessment of their seismic performance. This paper presents a 'toolkit' developed for bridge-specific fragility analysis of bridges; it is implemented on a "two-track" online platform, including ad-hoc developed software for online bridge-specific fragility curve derivation, as well as the option to select an appropriate set of generic fragility curves from a database including a broad range of bridge classes. Three alternative options for the estimation of component-specific limit state thresholds are provided; selection from extensive lists with available thresholds for piers, bearings and abutments, and calculation of limit state thresholds for as-built and retrofitted piers based on (a) closed-form relationships, or (b) inelastic pushover analysis and capacity assessment of a parametrically defined pier model (carried out online). Details regarding the software developed, the methodology for bridge-specific fragility curves, and all critical features are presented and discussed herein. The application of the online software is illustrated through two case studies involving the derivation of fragility curves for bridges with different structural systems and properties.
Earthquake Engineering & Structural Dynamics
Co-simulation techniques are widely used to enable global simulation of a coupled mechanical syst... more Co-simulation techniques are widely used to enable global simulation of a coupled mechanical system via composition of simulators. Within this work, the focus is initially placed on a new scheme for the numerical integration of each subsystem since the corresponding accuracy affects directly the correct solution of a decomposed model. Following that, the new co-simulation methods are introduced. Specifically, a novel coupling strategy for satisfying the coupling conditions in their integral (weak) form, in the time domain, is proposed. This formulation constitutes a general framework for the generation of coupling condition schemes with varying accuracy and stability properties, based on the choice of basis and order of polynomials for the involved quantities, thus creating a whole new perspective on the field of co-simulation. In addition, the point-collocation method, which is mainly employed in the literature, is easily recognized as a degenerate case of this general weak formula...
Proceedings of the 4th International Conference on Computational Methods in Structural Dynamics and Earthquake Engineering (COMPDYN 2013), 2014
A systematic theoretical approach is presented, in an effort to provide a complete and illuminati... more A systematic theoretical approach is presented, in an effort to provide a complete and illuminating study on motion of a rigid body rotating about a fixed point. Since the configuration space of this motion is a differentiable manifold possessing group properties, this approach is based on some fundamental concepts of differential geometry. Α key idea is the introduction of a canonical connection, matching the manifold and group properties of the configuration space. This is sufficient for performing the kinematics. Next, following the selection of an appropriate metric, the dynamics is also carried over. The present approach is theoretically more demanding than the traditional treatments but brings substantial benefits. In particular, an elegant interpretation is provided for all the quantities with fundamental importance in rigid body motion. It also leads to a correction of some misconceptions and geometrical inconsistencies in the field. Finally, it provides powerful insight and a strong basis for the development of efficient numerical techniques in problems involving large rotations.
International Journal of Solids and Structures, 2013
A systematic theoretical approach is presented, in an effort to provide a complete and illuminati... more A systematic theoretical approach is presented, in an effort to provide a complete and illuminating study on kinematics and dynamics of rigid bodies rotating about a fixed point. Specifically, this approach is based on some fundamental concepts of differential geometry, with particular reference to Lie group theory. This treatment is motivated by the form of the configuration space corresponding to large rigid body rotation, which is a differentiable manifold possessing group properties. First, the basic steps of the classical approach on the subject are briefly summarized. Then, some geometrical tools are presented, which are essential for supporting and illustrating the steps and findings of the new approach. Finally, the emphasis is placed on a thorough investigation of the problem of finite rotations. A key idea is the introduction of a canonical connection, matching the manifold and group properties of the configuration space. This proves to be sufficient and effective for performing the kinematics. Next, following the selection of an appropriate metric, the dynamics is also carried over. The present approach is theoretically more demanding than the traditional treatments in engineering but brings substantial benefits. In particular, an elegant interpretation is provided for all the quantities with fundamental importance in both rigid body kinematics and dynamics. Most importantly, this also leads to a correction of some misconceptions and geometrical inconsistencies in the field. Among other things, the deeper understanding of the theoretical concepts provides powerful insight and a strong basis for the development of efficient numerical techniques in problems of solid and structural mechanics involving large rotations.
Multibody System Dynamics
International Journal of Solids and Structures, 2020
This is a PDF file of an article that has undergone enhancements after acceptance, such as the ad... more This is a PDF file of an article that has undergone enhancements after acceptance, such as the addition of a cover page and metadata, and formatting for readability, but it is not yet the definitive version of record. This version will undergo additional copyediting, typesetting and review before it is published in its final form, but we are providing this version to give early visibility of the article. Please note that, during the production process, errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain.
Αριστοτέλειο Πανεπιστήμιο Θεσσαλονίκης (ΑΠΘ). Σχολή Πολυτεχνική. Τμήμα Πολιτικών Μηχανικών. Τομέας Επιστήμης και Τεχνολογίας των Κατασκευών, 2005
International Journal of Non-Linear Mechanics, 2021
Abstract This work presents a new numerical integration method for determining dynamics of a clas... more Abstract This work presents a new numerical integration method for determining dynamics of a class of multibody systems involving impact and friction. Specifically, these systems are subject to a set of equality constraints and can exhibit single frictional impact events. Such events are associated to significant numerical stiffness, appearing in the equations of motion. The new method is a time-stepping scheme, involving proper incorporation of a novel return mapping into an augmented Lagrangian formulation, developed recently for systems with bilateral constraints only. Namely, when an impact is detected during a time step, this map is applied at the end of the step in order to bring the system position back to the configuration manifold with the allowable motions. The construction of this map is based on the concept of Jacobi fields on non-flat manifolds. Moreover, once an impact event is detected, the post-impact state is determined by employing a combination of analytical and numerical tools. First, a proper coordinate transformation is performed, bringing the system into a new set of coordinates, which are suitable for describing the impact dynamics. In these coordinates, the dominant dynamics is described by a system of three equations of motion only, which are valid during the short contact interval. In addition, these equations are geometrically discretized by using appropriate cubic splines on the configuration manifold. In this way, the inherent numerical stiffness of the class of systems examined is properly addressed, since it is restricted to a space with a much smaller dimension and a much shorter time scale. Finally, the accuracy and efficiency of the new method is demonstrated by applying it to a selected set of mechanical examples.
NODYCON Conference Proceedings Series, 2022
International Journal of Solids and Structures, 2018
This study focuses on the development of a new formulation, which describes the dynamics of a cla... more This study focuses on the development of a new formulation, which describes the dynamics of a class of mechanical systems involving a single contact with friction. The whole process is performed within the general framework of analytical dynamics. At the same time, the efforts are assisted and enhanced by employing some fundamental tools of differential geometry. This provides a strong theoretical foundation, allowing for a systematic and consistent application of Newton's law of motion to systems possessing configuration manifolds with boundary. The manifold boundary is first defined by using the unilateral constraint representing the contact event. Then, it is shown that the corresponding contact phase takes place inside a thin layer near this boundary, where the dominant dynamics is described by a suitable set of three ordinary differential equations. The explicit appearance of time in the formulation introduces a short but finite time scale, which permits the consideration of contact of any combination of mechanical bodies, including rigid and discretized deformable bodies. Finally, the study concludes with presentation of a selected set of examples. In all cases, emphasis is put on illustrating the basic steps of the analysis as well as on capturing and investigating phenomena arising during central or eccentric collision of bodies.
Journal of Computational and Nonlinear Dynamics, 2018
A systematic theoretical approach is presented, revealing dynamics of a class of multibody system... more A systematic theoretical approach is presented, revealing dynamics of a class of multibody systems. Specifically, the motion is restricted by a set of bilateral constraints, acting simultaneously with a unilateral constraint, representing a frictional impact. The analysis is carried out within the framework of Analytical Dynamics and uses some concepts of differential geometry, which provides a foundation for applying Newton's second law. This permits a successful and illuminating description of the dynamics. Starting from the unilateral constraint, a boundary is defined, providing a subspace of allowable motions within the original configuration manifold. Then, the emphasis is focused on a thin boundary layer. In addition to the usual restrictions imposed on the tangent space, the bilateral constraints cause a correction of the direction where the main impulse occurs. When friction effects are negligible, the dominant action occurs along this direction and is described by a sin...
International Journal of Non-Linear Mechanics, 2017
This study presents a systematic approach, leading to a new set of equations of motion for a clas... more This study presents a systematic approach, leading to a new set of equations of motion for a class of mechanical systems subject to a single frictionless contact constraint. To achieve this goal, some fundamental concepts of b-geometry are utilized and adapted to the general framework of Analytical Dynamics. These concepts refer to the theory of manifolds with boundary and provide a suitable and strong theoretical foundation. First, the boundary is defined within the original configuration manifold of the system by the equality in the unilateral constraint. Then, an appropriate vector bundle is considered, involving only smooth vector fields, even at the boundary. After determining the essential geometric properties (i.e., the metric and the connection) near the boundary, Newton's law of motion is applied. In this way, the equations of motion during the contact phase are derived as a system of ordinary differential equations. These equations possess a special form inside a thin boundary layer. In particular, the essential dynamics of the systems examined is found to be governed by a single second order ordinary differential equation, which is investigated fully. Moreover, a critical comparison of the present formulation with the classical formulations applied to systems with a frictionless contact is performed. Finally, the effect of the dominant parameters on the dynamics during the contact phase and the steps for the application process to mechanical systems are illustrated by two selected examples, referring to contact of a particle and a rigid body with a plane.
Nonlinear Dynamics, 2016
This study is focused on a class of discrete mechanical systems subject to equality motion constr... more This study is focused on a class of discrete mechanical systems subject to equality motion constraints involving time and acatastatic terms. In addition, their original configuration manifold possesses time-dependent geometric properties. The emphasis is placed on a proper application of Newton's law of motion. A key step is to consider the corresponding event manifold, whose dimension is bigger by one than the configuration manifold, since a temporal coordinate is added to the original set of spatial coordinates. Then, its geometric properties are determined and Newton's law is applied on it, when no motion constraints exist. Next, the way of introducing time dependence in the geometric properties of the configuration manifold through a coordinate transformation in the event manifold is investigated and clarified. Moreover, similar time effects introduced through the motion constraints are also examined. Based on these and application of foliation theory, a geometric definition of a scleronomic manifold is then provided, accompanied by a set of coordinate invariant conditions. The analysis is completed by deriving an appropriate set of equations of motion on the original configuration manifold, when additional constraints are imposed. These equations appear as a system of second-order ordinary differential equations. Finally, the analytical findings are enhanced
Nonlinear Dynamics, 2013
This work is devoted to deriving and investigating conditions for the correct application of Newt... more This work is devoted to deriving and investigating conditions for the correct application of Newton's law to mechanical systems subjected to motion constraints. It utilizes some fundamental concepts of differential geometry and treats both holonomic and nonholonomic constraints. This approach is convenient since it permits one to view the motion of any dynamical system as a path of a point on a manifold. In particular, the main focus is on the establishment of appropriate conditions, so that the form of Newton's law of motion remains invariant when imposing an additional set of motion constraints on a mechanical system. Based on this requirement, two conditions are derived, specifying the metric and the form of the connection on the new manifold, which results after enforcing the additional constraints. The latter is weaker than a similar condition obtained by imposing a metric compatibility condition holding on Riemannian manifolds and employed frequently in the literature. This is shown to have several practical implications. First, it provides a valuable freedom for selecting the connection on the manifold describing large rigid body rotation, so that the group properties of this manifold are preserved. Moreover, it is used to state clearly the conditions for expressing Newton's law on
NODYCON Conference Proceedings Series, 2022
Co-simulation is used to enable global simulation of a coupled system via composition of simulato... more Co-simulation is used to enable global simulation of a coupled system via composition of simulators. Within this work, a co-simulation approach is developed and presented for mechanical systems with nonlinear components. Specifically, dynamics of a model two-degree-of-freedom oscillator, including Duffing type nonlinearities, is investigated first. The method of multiple time scales is applied and a set of averaged equations is derived for cases of primary external resonance, whose solution is then used as a reference solution. The main focus is placed on mechanical subsystems. However, the new method is developed so that it has general validity and can be applied to coupling arbitrary solvers.
A new numerical integration method is presented for a class of multibody systems, which exhibit s... more A new numerical integration method is presented for a class of multibody systems, which exhibit single frictional impacts. The new method is a time-stepping scheme, involving incorporation of a novel return map into an augmented Lagrangian formulation, developed recently for systems with bilateral constraints. When an impact is detected, this map is applied at the end of the step and brings the system position back to the configuration manifold with the allowable motions. In addition, the equations of motion during impact are geometrically discretized by appropriate cubic splines on the configuration manifold. Finally, the accuracy and efficiency of the method is demonstrated by a set of mechanical examples.
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Papers by Elias Paraskevopoulos