31.80 Angewandte Mathematik
Refine
Document Type
- Conference Proceeding (358)
- Article (261)
- Master's Thesis (3)
- Doctoral Thesis (2)
- Bachelor Thesis (1)
Institute
- Professur Informatik im Bauwesen (281)
- Institut für Strukturmechanik (ISM) (202)
- In Zusammenarbeit mit der Bauhaus-Universität Weimar (82)
- Professur Stochastik und Optimierung (42)
- Graduiertenkolleg 1462 (32)
- Professur Angewandte Mathematik (17)
- Institut für Konstruktiven Ingenieurbau (IKI) (4)
- Professur Baubetrieb und Bauverfahren (2)
- Professur Computer Vision in Engineering (2)
- Professur Modellierung und Simulation - Mechanik (2)
Keywords
- Angewandte Mathematik (328)
- Strukturmechanik (183)
- Computerunterstütztes Verfahren (153)
- Angewandte Informatik (146)
- Architektur <Informatik> (75)
- Computer Science Models in Engineering; Multiscale and Multiphysical Models; Scientific Computing (74)
- Modellierung (44)
- Stochastik (40)
- Building Information Modeling (35)
- CAD (35)
- Data, information and knowledge modeling in civil engineering; Function theoretic methods and PDE in engineering sciences; Mathematical methods for (robotics and) computer vision; Numerical modeling in engineering; Optimization in engineering applications (34)
- Finite-Elemente-Methode (28)
- Bauwerk (22)
- Optimierung (17)
- Tragwerk (17)
- Bauplanung (16)
- Bauwesen (12)
- Dreidimensionales Modell (12)
- Internet (12)
- Baustatik (11)
- Stahlbeton (11)
- Gebäude (10)
- Datenaustausch (9)
- Quaternion (9)
- Bruchmechanik (8)
- Nichtlineares Phänomen (8)
- Objektmodell (8)
- Schale (8)
- Mathematisches Modell (7)
- Bauaufnahme (6)
- Dynamische Belastung (6)
- Langzeitverhalten (6)
- Architektur (5)
- Bauteil (5)
- Beton (5)
- Datenerfassung (5)
- Datenmodell (5)
- Elastoplastizität (5)
- Informationsmanagement (5)
- Prozessmodell (5)
- Software (5)
- Tragverhalten (5)
- Transportproblem (5)
- Öffentlicher Personennahverkehr (5)
- Anwendung (4)
- Bauablauf (4)
- Bauablauf / Ablaufplanung (4)
- Baubetrieb (4)
- Entscheidung bei mehrfacher Zielsetzung (4)
- Gebäudeleittechnik (4)
- Projektmanagement (4)
- Schwingung (4)
- Sicherheit (4)
- Stochastisches Modell (4)
- Transportables Gerät (4)
- Verkehrsnetz (4)
- Zeitabhängigkeit (4)
- Zufallsvariable (4)
- Ablaufplanung (3)
- Bauausführung (3)
- Belastung (3)
- Bewehrung (3)
- Boden-Bauwerk-Wechselwirkung (3)
- Datenbank (3)
- Erdbebenbelastung (3)
- Fuzzy-Logik (3)
- Geotechnik (3)
- Gleichgewicht (3)
- Graphentheorie (3)
- Grenzzustand (3)
- Informatik (3)
- Ingenieurbau (3)
- Lernendes System (3)
- Maschinelles Lernen (3)
- Nichtlineare Mechanik (3)
- Numerisches Verfahren (3)
- Parameteridentifikation (3)
- Petri-Netz (3)
- Rissbildung (3)
- Stadtplanung (3)
- Stahlkonstruktion (3)
- Textilfaser (3)
- Visualisierung (3)
- Wahrscheinlichkeitsrechnung (3)
- Wavelet (3)
- Zuverlässigkeit (3)
- Algorithmus (2)
- Ausschreibung (2)
- Aussteifung (2)
- Bauphysik (2)
- Bauschaden (2)
- Bauvorhaben (2)
- Bauzeichnung (2)
- Bewertung (2)
- Bildverarbeitung (2)
- Bodenmechanik (2)
- Computerunterstützter Unterricht (2)
- Datenverwaltung (2)
- Dialogsystem (2)
- Digitalisierung (2)
- Diskrete Optimierung (2)
- Dokumentenverwaltungssystem (2)
- Dynamik (2)
- Dünnwandiges Bauelement (2)
- Eigenwert (2)
- Facility-Management (2)
- Festkörpermechanik (2)
- Flüssigkeit-Bauwerk-Wechselwirkung (2)
- Freie Schwingung (2)
- Genetischer Algorithmus (2)
- Geschichtetes Medium (2)
- Informationstechnik (2)
- Instandhaltung (2)
- Kalkulation (2)
- Kontinuum (2)
- Kooperatives Informationssystem (2)
- Lebensdauer (2)
- Management (2)
- Marketing (2)
- Mathematik (2)
- Matrizenrechnung (2)
- Mechanische Eigenschaft (2)
- Netzwerk (2)
- Orthotropes Bauteil (2)
- Planung (2)
- Plastizitätstheorie (2)
- Platte (2)
- Produktionsplanung (2)
- Prozessoptimierung (2)
- Rahmentragwerk (2)
- Raumtragwerk (2)
- Rechnernetz (2)
- Reihenfolgeproblem (2)
- Rekonstruktion (2)
- Sandwichbauweise (2)
- Stabilität (2)
- Standardisierung (2)
- Strukturanalyse (2)
- Transfer learning (2)
- Umweltfaktor (2)
- Virtuelle Realität (2)
- Virtuelles Unternehmen (2)
- Windlast (2)
- XML (2)
- 3D reinforced concrete buildings (1)
- ANSYS (1)
- Activation function (1)
- Amplitude (1)
- Approximation (1)
- Arc-direct energy deposition (1)
- Aufwindkraftwerk (1)
- Automatisiertes System (1)
- Balken (1)
- Bauentwurf (1)
- Baugrund (1)
- Bauingenieurstudium (1)
- Baustahl (1)
- Bautechnik (1)
- Bauwerk / Technische Überwachung (1)
- Bauzustand (1)
- Bedarfsermittlung (1)
- Beleuchtung (1)
- Beltrami-Gleichung (1)
- Benutzer / Beteiligung (1)
- Benutzer-entworfene Wohnungen (1)
- Benutzeroberfläche (1)
- Berechnung (1)
- Berlin (1)
- Berührungslose Messung (1)
- Beschränkung (1)
- Betonbrücke (1)
- Betriebswirtschaft (1)
- Beulung (1)
- Beurteilung (1)
- Bewertungssystem (1)
- Bewirtschaftung (1)
- Biegemoment (1)
- Bildanalyse (1)
- Bogenbrücke (1)
- Bogenstaumauer (1)
- Brandgefahr (1)
- Brandschutz (1)
- Brücke (1)
- Brückenbau (1)
- Building Object Model (1)
- Busspur (1)
- CAD / Architektur (1)
- CAE (1)
- Cauchy-Riemannsche Differentialgleichungen (1)
- Chaostheorie (1)
- Chirale Verbindungen (1)
- Clifford-Analysis (1)
- Collocation method (1)
- Computer Supported Cooperative Work (1)
- Computergestütztes Verfahren (1)
- Computergraphik (1)
- Computersimulation (1)
- Controlling (1)
- Darstellungssatz von Goursat (1)
- Data, information and knowledge modeling in civil engineering (1)
- Datenbankverwaltung (1)
- Dateneingabegerät (1)
- Deep Learning (1)
- Deep learning (1)
- Demontage (1)
- Dialogprogrammierung (1)
- Dickwandiges Bauelement (1)
- Differentialoperator (1)
- Digitales Bautagebuch (1)
- Digitales Modell (1)
- Dirac-Gleichung (1)
- Diskrete Fourier-Transformation (1)
- Domain Adaptation (1)
- Dreieck (1)
- Druckbelastung (1)
- Dual phase steel (1)
- Dual-support (1)
- Early design stage (1)
- Eigenwertproblem (1)
- Einfamilienhaus (1)
- Einsturz (1)
- Eisenbahnbrücke (1)
- Elastizitätstheorie (1)
- Elastomer (1)
- Elektromagnetisches Feld (1)
- Ellipsoid (1)
- Energiemanagement (1)
- Energieversorgung (1)
- Entscheidungstheorie (1)
- Entscheidungsunterstützungssystem (1)
- Entwurf (1)
- Erdbebenschutz (1)
- Expertensystem (1)
- FEM (1)
- Fachwerkbau (1)
- Faktor <Algebra> (1)
- Fehlerabschätzung (1)
- Fertigbau (1)
- Finite-Streifen (1)
- Finite-Streifen-Methode (1)
- Fourier (1)
- Fourier-Reihe (1)
- Fraktal (1)
- Function theoretic methods and PDE in engineering sciences (1)
- Funktionentheorie (1)
- Funktionsraum / Mathematik (1)
- Fuzzifizierung (1)
- Fuzzy-Optimierung (1)
- Gebäudeleitsystem (1)
- Generelle-Interessen-Skala (1)
- Geographic Information System (1)
- Gesamtbauwerk (1)
- Geschossbau (1)
- Gestaltoptimierung (1)
- Gittererzeugung (1)
- Graph (1)
- Green-Funktion (1)
- Grenzlast (1)
- Großtafelbau (1)
- Grundwasser (1)
- Gruppentheorie (1)
- Gründung (1)
- Halbraum (1)
- Hamilton-Operator (1)
- Haus (1)
- Heizung (1)
- Hermitesche Entwicklung (1)
- Heuristik (1)
- Himmelslichtquotient (1)
- Holzkonstruktion (1)
- Hydrodynamik (1)
- Hyperkomplexe Funktion (1)
- IFC (1)
- Immobilienwirtschaft (1)
- Implicit (1)
- Industriepark (1)
- Informationssystem (1)
- Ingenieurbüro (1)
- Ingenieurholzbau (1)
- Ingenieurwissenschaften (1)
- Integrierte Planung (1)
- Intelligentes System (1)
- Investitionsplanung (1)
- Isotropie (1)
- Iteration (1)
- Kapitalwertmethode (1)
- Kartierung (1)
- Katalog (1)
- Kennzahl (1)
- Kernel <Informatik> (1)
- Klein- und Mittelbetrieb (1)
- Klein- und mittelstädtisches Unternehmen (1)
- Kollokationsmethode (1)
- Kommunikationstechnik (1)
- Komplexe Funktion (1)
- Konforme Abbildung (1)
- Kooperatives Arbeiten (1)
- Kostenanalyse (1)
- Kraftmethode (1)
- Kran (1)
- Kreis (1)
- Kriechen (1)
- Kuppel (1)
- Künstliche Intelligenz (1)
- Laplace-Operator (1)
- Laplace-Transformation (1)
- Laurent (1)
- Laurent-Reihe (1)
- Lebenszyklus <Wirtschaft> (1)
- Lebenszykluskonzept (1)
- Lehrter Bahnhof (1)
- Leitsystem (1)
- Lineare Elastizitätstheorie (1)
- Lüftung (1)
- Materialermüdung (1)
- Materialverhalten (1)
- Mathematical methods for (robotics and) computer vision (1)
- Mathematische Modellierung (1)
- Mathematische Physik (1)
- Mauerwerk (1)
- Maxwellsche Gleichungen (1)
- Mehrdimensionalität (1)
- Mehrkriterielle Optimierung (1)
- Mensch-Maschine-Kommunikation (1)
- Messtechnik (1)
- Metall verarbeitende Industrie (1)
- Mild steel (1)
- Modalanalyse (1)
- Monte-Carlo-Simulation (1)
- Multiobjective Optimization (1)
- Multiresolution analysis (1)
- NURBS (1)
- NURBS geometry (1)
- Navier-Stokes-Gleichung (1)
- Navier–Stokes equations (1)
- Netzplantechnik (1)
- Netzwerktheorie (1)
- Neuronales Lernen (1)
- Neuronales Netz (1)
- Nichtlineare Optimierung (1)
- Nichtlineare partielle Differentialgleichung (1)
- Nichtlineares System (1)
- Nichtlinearität (1)
- Niedrigenergiehaus (1)
- Nonlocal operator method (1)
- Numerical modeling in engineering (1)
- Nutzungsänderung (1)
- Näherungsverfahren (1)
- OA-Publikationsfonds2023 (1)
- OIP (1)
- OPL (1)
- Oberfläche (1)
- Objektorientierte Programmierung (1)
- Objektorientiertes Datenbanksystem (1)
- Operations Research (1)
- Operator energy functional (1)
- Opimization (1)
- Optimization in engineering applications (1)
- Passivhaus (1)
- Pflasterungen (Mathematik) (1)
- Photogrammetrie (1)
- Planungswerkzeugen (1)
- Plastische Deformation (1)
- Plausibilität (1)
- Polyharmonische Funktion (1)
- Polymorphie (1)
- Polystyrol (1)
- Potential problem (1)
- Produktinformation (1)
- Produktionssteuerung (1)
- Produktmodell (1)
- Prognose (1)
- Programm (1)
- Progressive Planung (1)
- Projektdokumentation (1)
- Projektfinanzierung (1)
- Projektierungsbetrieb (1)
- Projektplanung (1)
- Projektsteuerung (1)
- Prozessmanagement (1)
- Prozesssimulation (1)
- Qp-spaces (1)
- Quantenphysik (1)
- Randelemente-Methode (1)
- Randspannung (1)
- Raumordnung (1)
- Rechteck (1)
- Regelungssystem (1)
- Regelungstechnik (1)
- Regenwasser (1)
- Regressionsanalyse (1)
- Reparatur (1)
- Ressourcenallokation (1)
- Revitalisierung (1)
- Revitalization (1)
- Rippendecke (1)
- Riss (1)
- SDOF (1)
- Sandwichbauteil (1)
- Scalarization Methods (1)
- Schalenelement (1)
- Schalung (1)
- Schnittstelle (1)
- Schwingungsdämpfer (1)
- Setzung (1)
- Sichtbeton (1)
- Softwareengineering (1)
- Softwaresystem (1)
- Sonnenenergie (1)
- Sonnenscheindauer (1)
- Sonnenstrahlung (1)
- Spannender Baum (1)
- Spannung (1)
- Spannungs-Dehnungs-Beziehung (1)
- Spannungsintensitätsfaktor (1)
- Spline-Approximation (1)
- Stabilisierung (1)
- Stabwerk (1)
- Stadtentwässerung (1)
- Stadtverkehr (1)
- Stahlbau (1)
- Stahlbetonbauteil (1)
- Stahlbetonkonstruktion (1)
- Standortplanung (1)
- Stapelproblem (1)
- Statische Last (1)
- Steifigkeit (1)
- Stiffness matrix (1)
- Stochastischer Prozess (1)
- Stoffeigenschaft (1)
- Stoffgesetz (1)
- Stoffkreislauf (1)
- Stokes-Problem (1)
- Straße (1)
- Straßenbau (1)
- Stress-strain curve (1)
- Structural Optimization (1)
- Strömungsmechanik (1)
- Supply Chain Management (1)
- Synchronisierung (1)
- Systemidentifikation (1)
- TPOGS (1)
- Tafelbau (1)
- Talsperre (1)
- Taylor (1)
- Taylor series expansion (1)
- Taylor-Reihe (1)
- Teamorganisation (1)
- Temperatur (1)
- Theorie zweiter Ordnung (1)
- Trajektorie (Mathematik) (1)
- Transformation (1)
- Trassierung (1)
- Trägheit (1)
- Tunnel (1)
- Umbau (1)
- Umnutzung (1)
- Unsicherheit (1)
- Unternehmen / Organisation (1)
- Variantenvergleich (1)
- Variational principle (1)
- Variationsrechnung (1)
- Vektorfunktion (1)
- Verbundbauweise (1)
- Verbundtragwerk (1)
- Verbundwerkstoff (1)
- Verkehrsaufkommen (1)
- Verkehrsleitsystem (1)
- Verkehrsmittelwahl (1)
- Verkehrsplanung (1)
- Vernetztes System (1)
- Versagen (1)
- Versorgungsnetz (1)
- Verteiltes Datenbanksystem (1)
- Verteiltes Datenverarbeitungssystem (1)
- Verteiltes Softwaresystem (1)
- Viereck (1)
- Viskoelastisches Gelenk (1)
- Viskoplastizität (1)
- Vorfertigung (1)
- Vorspannung (1)
- Wand (1)
- Wartezeit (1)
- Wechselwirkung (1)
- Weimar / Herzogin-Anna-Amalia-Bibliothek (1)
- Weimar / Sonderforschungsbereich Werkstoffe und Konstruktionen für die Revitalisierung von Bauwerken (1)
- Wirtschaftlichkeit (1)
- Wohnung (1)
- Wärmeleitung (1)
- Wärmeleitungsgleichung (1)
- Wärmestrom (1)
- Wärmeübergang (1)
- Wärmeübertragung (1)
- Zeitrestriktion (1)
- Zugstab (1)
- Zusammengesetzte Fließbedingung (1)
- Zuverlässigkeitstheorie (1)
- abstraction (1)
- analytische Lösung (1)
- anforderungsorientierte Projektabwicklung (1)
- ans (1)
- anti-locking (1)
- assumed-natural-strain (1)
- building (1)
- computational modeling (1)
- decision making (1)
- deep learning (1)
- discrete fourier transform (1)
- discrete fundamental solution (1)
- diskrete Fourier-Transformation (1)
- dual-support (1)
- eindimensionale Wärmeleitung (1)
- engineering (1)
- experimental validation (1)
- finite element method (1)
- fisher-information matrix (1)
- formal approaches (1)
- foundation (1)
- function spaces (1)
- functionally graded materials (1)
- generalized Kolosov-Muskhelishvili formulae (1)
- generalized theorem of Goursat (1)
- geschichtete Wände (1)
- ground structure (1)
- große Rotationen (1)
- heat transfer (1)
- hybride Werkstoffe (1)
- internetbasierte Projektplattform (1)
- isoparametrisch (1)
- laplace operator (1)
- mean-squared error (1)
- mehrschichtige Wände (1)
- modelling (1)
- monogene Orthogonalreihenentwicklungen (1)
- monogenic orthogonal series expansions Fourier (1)
- multi-criterion analysis (1)
- neural architecture search (1)
- nichtlinear (1)
- nonlinear calculation (1)
- nonlocal Hessian operator (1)
- nonlocal operator method (1)
- nonlocal theory (1)
- numerical modelling (1)
- operator energy functional (1)
- physics-informed activation function (1)
- polymorphe Unschärfemodellierung (1)
- randomized spectral representation (1)
- rectangular lattice (1)
- shell (1)
- three-dimensional truss structures (1)
- topology optimization (1)
- tower-like structures (1)
- type theory (1)
- variational principle (1)
- verallgemeinerte Kolosov-Muskhelishvili Formeln (1)
- vibration-based methodology (1)
- Änderung (1)
- Überwachung (1)
The study presents a Machine Learning (ML)-based framework designed to forecast the stress-strain relationship of arc-direct energy deposited mild steel. Based on microstructural characteristics previously extracted using microscopy and X-ray diffraction, approximately 1000 new parameter sets are generated by applying the Latin Hypercube Sampling Method (LHSM). For each parameter set, a Representative Volume Element (RVE) is synthetically created via Voronoi Tessellation. Input raw data for ML-based algorithms comprises these parameter sets or RVE-images, while output raw data includes their corresponding stress-strain relationships calculated after a Finite Element (FE) procedure. Input data undergoes preprocessing involving standardization, feature selection, and image resizing. Similarly, the stress-strain curves, initially unsuitable for training traditional ML algorithms, are preprocessed using cubic splines and occasionally Principal Component Analysis (PCA). The later part of the study focuses on employing multiple ML algorithms, utilizing two main models. The first model predicts stress-strain curves based on microstructural parameters, while the second model does so solely from RVE images. The most accurate prediction yields a Root Mean Squared Error of around 5 MPa, approximately 1% of the yield stress. This outcome suggests that ML models offer precise and efficient methods for characterizing dual-phase steels, establishing a framework for accurate results in material analysis.
Identification of modal parameters of a space frame structure is a complex assignment due to a large number of degrees of freedom, close natural frequencies, and different vibrating mechanisms. Research has been carried out on the modal identification of rather simple truss structures. So far, less attention has been given to complex three-dimensional truss structures. This work develops a vibration-based methodology for determining modal information of three-dimensional space truss structures. The method uses a relatively complex space truss structure for its verification. Numerical modelling of the system gives modal information about the expected vibration behaviour. The identification process involves closely spaced modes that are characterised by local and global vibration mechanisms. To distinguish between local and global vibrations of the system, modal strain energies are used as an indicator. The experimental validation, which incorporated a modal analysis employing the stochastic subspace identification method, has confirmed that considering relatively high model orders is required to identify specific mode shapes. Especially in the case of the determination of local deformation modes of space truss members, higher model orders have to be taken into account than in the modal identification of most other types of structures.
As an optimization that starts from a randomly selected structure generally does not guarantee reasonable optimality, the use of a systemic approach, named the ground structure, is widely accepted in steel-made truss and frame structural design. However, in the case of reinforced concrete (RC) structural optimization, because of the orthogonal orientation of structural members, randomly chosen or architect-sketched framing is used. Such a one-time fixed layout trend, in addition to its lack of a systemic approach, does not necessarily guarantee optimality. In this study, an approach for generating a candidate ground structure to be used for cost or weight minimization of 3D RC building structures with included slabs is developed. A multiobjective function at the floor optimization stage and a single objective function at the frame optimization stage are considered. A particle swarm optimization (PSO) method is employed for selecting the optimal ground structure. This method enables generating a simple, yet potential, real-world representation of topologically preoptimized ground structure while both structural and main architectural requirements are considered. This is supported by a case study for different floor domain sizes.
We present a physics-informed deep learning model for the transient heat transfer analysis of three-dimensional functionally graded materials (FGMs) employing a Runge–Kutta discrete time scheme. Firstly, the governing equation, associated boundary conditions and the initial condition for transient heat transfer analysis of FGMs with exponential material variations are presented. Then, the deep collocation method with the Runge–Kutta integration scheme for transient analysis is introduced. The prior physics that helps to generalize the physics-informed deep learning model is introduced by constraining the temperature variable with discrete time schemes and initial/boundary conditions. Further the fitted activation functions suitable for dynamic analysis are presented. Finally, we validate our approach through several numerical examples on FGMs with irregular shapes and a variety of boundary conditions. From numerical experiments, the predicted results with PIDL demonstrate well agreement with analytical solutions and other numerical methods in predicting of both temperature and flux distributions and can be adaptive to transient analysis of FGMs with different shapes, which can be the promising surrogate model in transient dynamic analysis.
Nonlocal theories concern the interaction of objects, which are separated in space. Classical examples are Coulomb’s law or Newton’s law of universal gravitation. They had signficiant impact in physics and engineering. One classical application in mechanics is the failure of quasi-brittle materials. While local models lead to an ill-posed boundary value problem and associated mesh dependent results, nonlocal models guarantee the well-posedness and are furthermore relatively easy to implement into commercial computational software.
In this work, we present a deep collocation method (DCM) for three-dimensional potential problems in non-homogeneous media. This approach utilizes a physics-informed neural network with material transfer learning reducing the solution of the non-homogeneous partial differential equations to an optimization problem. We tested different configurations of the physics-informed neural network including smooth activation functions, sampling methods for collocation points generation and combined optimizers. A material transfer learning technique is utilized for non-homogeneous media with different material gradations and parameters, which enhance the generality and robustness of the proposed method. In order to identify the most influential parameters of the network configuration, we carried out a global sensitivity analysis. Finally, we provide a convergence proof of our DCM. The approach is validated through several benchmark problems, also testing different material variations.
In machine learning, if the training data is independently and identically distributed as the test data then a trained model can make an accurate predictions for new samples of data. Conventional machine learning has a strong dependence on massive amounts of training data which are domain specific to understand their latent patterns. In contrast, Domain adaptation and Transfer learning methods are sub-fields within machine learning that are concerned with solving the inescapable problem of insufficient training data by relaxing the domain dependence hypothesis. In this contribution, this issue has been addressed and by making a novel combination of both the methods we develop a computationally efficient and practical algorithm to solve boundary value problems based on nonlinear partial differential equations. We adopt a meshfree analysis framework to integrate the prevailing geometric modelling techniques based on NURBS and present an enhanced deep collocation approach that also plays an important role in the accuracy of solutions. We start with a brief introduction on how these methods expand upon this framework. We observe an excellent agreement between these methods and have shown that how fine-tuning a pre-trained network to a specialized domain may lead to an outstanding performance compare to the existing ones. As proof of concept, we illustrate the performance of our proposed model on several benchmark problems.
In this paper, we present an open-source code for the first-order and higher-order nonlocal operator method (NOM) including a detailed description of the implementation. The NOM is based on so-called support, dual-support, nonlocal operators, and an operate energy functional ensuring stability. The nonlocal operator is a generalization of the conventional differential operators. Combined with the method of weighed residuals and variational principles, NOM establishes the residual and tangent stiffness matrix of operate energy functional through some simple matrix without the need of shape functions as in other classical computational methods such as FEM. NOM only requires the definition of the energy drastically simplifying its implementation. The implementation in this paper is focused on linear elastic solids for sake of conciseness through the NOM can handle more complex nonlinear problems. The NOM can be very flexible and efficient to solve partial differential equations (PDEs), it’s also quite easy for readers to use the NOM and extend it to solve other complicated physical phenomena described by one or a set of PDEs. Finally, we present some classical benchmark problems including the classical cantilever beam and plate-with-a-hole problem, and we also make an extension of this method to solve complicated problems including phase-field fracture modeling and gradient elasticity material.
In this study, we propose a nonlocal operator method (NOM) for the dynamic analysis of (thin) Kirchhoff plates. The nonlocal Hessian operator is derived based on a second-order Taylor series expansion. The NOM does not require any shape functions and associated derivatives as ’classical’ approaches such as FEM, drastically facilitating the implementation. Furthermore, NOM is higher order continuous, which is exploited for thin plate analysis that requires C1 continuity. The nonlocal dynamic governing formulation and operator energy functional for Kirchhoff plates are derived from a variational principle. The Verlet-velocity algorithm is used for the time discretization. After confirming the accuracy of the nonlocal Hessian operator, several numerical examples are simulated by the nonlocal dynamic Kirchhoff plate formulation.
We present a stochastic deep collocation method (DCM) based on neural architecture search (NAS) and transfer learning for heterogeneous porous media. We first carry out a sensitivity analysis to determine the key hyper-parameters of the network to reduce the search space and subsequently employ hyper-parameter optimization to finally obtain the parameter values. The presented NAS based DCM also saves the weights and biases of the most favorable architectures, which is then used in the fine-tuning process. We also employ transfer learning techniques to drastically reduce the computational cost. The presented DCM is then applied to the stochastic analysis of heterogeneous porous material. Therefore, a three dimensional stochastic flow model is built providing a benchmark to the simulation of groundwater flow in highly heterogeneous aquifers. The performance of the presented NAS based DCM is verified in different dimensions using the method of manufactured solutions. We show that it significantly outperforms finite difference methods in both accuracy and computational cost.