Application of Solution Structure Method to Modeling Dynamic Response of Mechanical Structures

Transient nature of the loading conditions applied to the structural components makes dynamic analysis one of the important components in the design-analysis cycle. Time-varying forces and accelerations can substantially change stress distributions and cause a premature failure of the mechanical structures. In addition, it is also important to determine dynamic response of the structural elements to the frequency of the applied loads. In this paper we describe an application of the meshfree Solution Structure Method to the structural dynamics problems. Solution Structure Method is a meshfree method which enables construction of the solutions to the engineering problems that satisfy exactly all prescribed boundary conditions. This method is capable of using spatial meshes that do not conform to the shape of a geometric model. Instead of using the grid nodes to enforce boundary conditions, it employs distance fields to the geometric boundaries and combines them with the basis functions and prescribed boundary conditions at run time. This defines unprecedented geometric flexibility of the Solution Structure Method as well as the complete automation of the solution procedure

Controlling the Error on Target Motion through Real-time Mesh Adaptation: Applications to Deep Brain Stimulation

We present an error-controlled mesh refinement procedure for needle insertion simulation and apply it to the simulation of electrode implantation for deep brain stimulation, including brain shift. Our approach enables to control the error in the computation of the displacement and stress fields around the needle tip and needle shaft by suitably refining the mesh, whilst maintaining a coarser mesh in other parts of the domain. We demonstrate through academic and practical examples that our approach increases the accuracy of the displacement and stress fields around the needle without increasing the computational expense. This enables real-time simulations. The proposed methodology has direct implications to increase the accuracy and control the computational expense of the simulation of percutaneous procedures such as biopsy, brachytherapy, regional anesthesia, or cryotherapy and can be essential to the development of robotic guidance.Comment: 21 pages, 14 figure

Heterogeneous Material Modeling with Distance Fields

We propose a universal approach to the outstanding problem of computer modeling of continuously varying distributions of material properties satisfying prescribed material quantities and rates on a finite collection of geometric features. The central notion is a parameterization of the shape’s interior by distances from the material features - either exactly or approximately; this parameterization supports specification, interpolation, and optimization of desired material distributions in a systematic and controlled fashion. We demonstrate how the approach can be implemented within the existing framework of solid modeling and its numerous advantages, including: • precise and intuitive control using explicit, analytic, differential, and integral constraints specified on the original (not discretized) geometric model; • applicability to material features of arbitrary dimension, shape, and topology; and • guaranteed smoothness and analytic properties for superior performance, analysis and optimization. Last, but not least, the proposed approach subsumes and generalizes a number of other proposals for heterogeneous material modeling for FGM, heterogeneous solid modeling, and solid free-form fabrication.Mechanical Engineerin

Modelling High Speed Machining with the SPH Method

The purpose of this work is to evaluate the use of the Smoothed Particle Hydrodynamics (SPH) method within the framework of high speed cutting modelling. First, a 2D SPH based model is carried out using the LS-DYNA® software. SPH is a meshless method, thus large material distortions that occur in the cutting problem are easily managed and SPH contact control allows a “natural” workpiece/chip separation. The developed SPH model proves its ability to account for continuous and shear localized chip formation and also correctly estimates the cutting forces, as illustrated in some orthogonal cutting examples. Then, The SPH model is used in order to improve the general understanding of machining with worn tools. At last, a milling model allowing the calculation of the 3D cutting forces is presented. The interest of the suggested approach is to be freed from classically needed machining tests: Those are replaced by 2D numerical tests using the SPH model. The developed approach proved its ability to model the 3D cutting forces in ball end milling

Investigation of the use of meshfree methods for haptic thermal management of design and simulation of MEMS

This thesis presents a novel approach of using haptic sensing technology combined with virtual environment (VE) for the thermal management of Micro-Electro-Mechanical-Systems (MEMS) design. The goal is to reduce the development cycle by avoiding the costly iterative prototyping procedure. In this regard, we use haptic feedback with virtua lprototyping along with an immersing environment. We also aim to improve the productivity and capability of the designer to better grasp the phenomena operating at the micro-scale level, as well as to augment computational steering through haptic channels. To validate the concept of haptic thermal management, we have implemented a demonstrator with a user friendly interface which allows to intuitively "feel" the temperature field through our concept of haptic texturing. The temperature field in a simple MEMS component is modeled using finite element methods (FEM) or finite difference method (FDM) and the user is able to feel thermal expansion using a combination of different haptic feedback. In haptic application, the force rendering loop needs to be updated at a frequency of 1Khz in order to maintain continuity in the user perception. When using FEM or FDM for our three-dimensional model, the computational cost increases rapidly as the mesh size is reduced to ensure accuracy. Hence, it constrains the complexity of the physical model to approximate temperature or stress field solution. It would also be difficult to generate or refine the mesh in real time for CAD process. In order to circumvent the limitations due to the use of conventional mesh-based techniques and to avoid the bothersome task of generating and refining the mesh, we investigate the potential of meshfree methods in the context of our haptic application. We review and compare the different meshfree formulations against FEM mesh based technique. We have implemented the different methods for benchmarking thermal conduction and elastic problems. The main work of this thesis is to determine the relevance of the meshfree option in terms of flexibility of design and computational charge for haptic physical model

Thermo-mechanical modeling for selective laser melting

Selective Laser Melting (SLM) is an Additive Manufacturing (AM) process where a powder bed is locally melted with a laser. Layer by layer, complex three dimensional geometries including overhangs can be produced. Up to date, the material and process development of SLM mainly relies on experimental studies that are time intensive and costly. Simulation tools offer the potential to gain a deeper understanding of the process - structure - property interaction. This can help to find optimal process parameters for individualized components and the processing of innovative powder materials. In this work, a rigorous thermo-mechanical framework for the finite deformation phase change problem is formulated. Beside the phase change, an additional peculiarity of the SLM process is the fusion of powder particles. Regarding the numerical solution, meshfree methods seem to be especially suited because the treatment of particle fusion is intrinsic to the formulation. The complex moving boundaries between liquid melt and solid metal can be resolved without additional numerical effort. The recently introduced Optimal Transportation Meshfree Method (OTM) has been chosen since it was promoted as a versatile tool for both fluid and solid mechanics. Special focus lays on the modeling of laser-matter interaction. The laser beam can be divided into moving discrete energy portions (rays) that are traced in space and time. In order to compute the reflection and absorption, usually a triangulation of the free surface is conducted. Within meshfree methods, this is a very expensive operation. To avoid the need for surface triangulation, a computationally efficient algorithm is presented which can easily be combined with meshfree methods. Both melt pool dynamics and residual stress formation are studied with the developed numerical framework. The influence of laser heating and cooling conditions on melting and consolidation is investigated. Although the numerical results are promising, it was found that the OTM exhibits some limitations. Therefore, the accuracy of the method is critically discussed

Mixed peridynamic formulations for compressible and incompressible finite deformations

The large flexibility of meshfree solution schemes makes them attractive for many kinds of engineering applications, like Additive Manufacturing or cutting processes. While numerous meshfree methods were developed over the years, the accuracy and robustness are still challenging and critical issues. Stabilization techniques of various kinds are typically used to overcome these problems, but often require the tuning of unphysical parameters. The Peridynamic Petrov–Galerkin method is a generalization of the peridynamic theory of correspondence materials and offers a stable and robust alternative. In this work, the stabilization free approach is extended to three dimensional problems of finite elasticity. Locking-free mixed formulations for nearly incompressible and incompressible materials are developed and investigated in convergence studies. In general, an efficient implicit quasi-static framework based on Automatic Differentiation is presented. The numerical examples highlight the convergence properties and robustness of the proposed formulations. © 2020, The Author(s)

DIGITAL SURVEY AI AND SEMANTICS FOR RAILWAY MASONRY BRIDGES HEALTH ASSESSMENT

Abstract. Masonry arch railway bridges represent a historically built heritage to be preserved. The multidisciplinary approach requires the construction of a common language, namely the creation of a formal conceptualisation of bridge domain that could serve as basis for both adding new layers of knowledge in H-BIM modeling and aiding the automatic segmentation of masonry bridge point clouds, thus supporting the semi-automatic creation of information models. The presented research aims at showing the results of an in-depth analysis conducted on masonry arched bridges computational ontologies; following this, the authors propose a semantic conceptualization in the masonry bridge domain, structured with three group of key concepts needed in the process of knowledge: bridge elements, materials, and defects. As a case study the masonry bridges of the Sicilian Circumetnea railway are chosen

Peridynamic Galerkin methods for nonlinear solid mechanics

Simulation-driven product development is nowadays an essential part in the industrial digitalization. Notably, there is an increasing interest in realistic high-fidelity simulation methods in the fast-growing field of additive and ablative manufacturing processes. Thanks to their flexibility, meshfree solution methods are particularly suitable for simulating the stated processes, often accompanied by large deformations, variable discontinuities, or phase changes. Furthermore, in the industrial domain, the meshing of complex geometries represents a significant workload, which is usually minor for meshfree methods. Over the years, several meshfree schemes have been developed. Nevertheless, along with their flexibility in discretization, meshfree methods often endure a decrease in accuracy, efficiency and stability or suffer from a significantly increased computation time. Peridynamics is an alternative theory to local continuum mechanics for describing partial differential equations in a non-local integro-differential form. The combination of the so-called peridynamic correspondence formulation with a particle discretization yields a flexible meshfree simulation method, though does not lead to reliable results without further treatment.\newline In order to develop a reliable, robust and still flexible meshfree simulation method, the classical correspondence formulation is generalized into the Peridynamic Galerkin (PG) methods in this work. On this basis, conditions on the meshfree shape functions of virtual and actual displacement are presented, which allow an accurate imposition of force and displacement boundary conditions and lead to stability and optimal convergence rates. Based on Taylor expansions moving with the evaluation point, special shape functions are introduced that satisfy all the previously mentioned requirements employing correction schemes. In addition to displacement-based formulations, a variety of stabilized, mixed and enriched variants are developed, which are tailored in their application to the nearly incompressible and elasto-plastic finite deformation of solids, highlighting the broad design scope within the PG methods. Extensive numerical validations and benchmark simulations are performed to show the impact of violating different shape function requirements as well as demonstrating the properties of the different PG formulations. Compared to related Finite Element formulations, the PG methods exhibit similar convergence properties. Furthermore, an increased computation time due to non-locality is counterbalanced by a considerably improved robustness against poorly meshed discretizations

The Neural Particle Method -- An Updated Lagrangian Physics Informed Neural Network for Computational Fluid Dynamics

Numerical simulation is indispensable in industrial design processes. It can replace expensive experiments and even reduce the need for prototypes. While products designed with the aid of numerical simulation undergo continuous improvement, this must also be true for numerical simulation itself. Up to date, no general purpose numerical method is available which can accurately resolve a variety of physics ranging from fluid to solid mechanics including large deformations and free surface flow phenomena. These complex multi-physics problems occur for example in Additive Manufacturing processes. In this sense, the recent developments in Machine Learning display promise for numerical simulation. It has recently been shown that instead of solving a system of equations as in standard numerical methods, a neural network can be trained solely based on initial and boundary conditions. Neural networks are smooth, differentiable functions that can be used as a global ansatz for Partial Differential Equations (PDEs). While this idea dates back to more than 20 years ago [Lagaris et al., 1998], it is only recently that an approach for the solution of time dependent problems has been developed [Raissi et al., 2019]. With the latter, implicit Runge Kutta schemes with unprecedented high order have been constructed to solve scalar-valued PDEs. We build on the aforementioned work in order to develop an Updated Lagrangian method for the solution of incompressible free surface flow subject to the inviscid Euler equations. The method is easy to implement and does not require any specific algorithmic treatment which is usually necessary to accurately resolve the incompressibility constraint. Due to its meshfree character, we will name it the Neural Particle Method (NPM). It will be demonstrated that the NPM remains stable and accurate even if the location of discretization points is highly irregular.Comment: In review by Computer Methods in Applied Mechanics and Engineerin