119 research outputs found
Boundary-Conforming Free-Surface Flow Computations: Interface Tracking for Linear, Higher-Order and Isogeometric Finite Elements
The simulation of certain flow problems requires a means for modeling a free
fluid surface; examples being viscoelastic die swell or fluid sloshing in
tanks. In a finite-element context, this type of problem can, among many other
options, be dealt with using an interface-tracking approach with the
Deforming-Spatial-Domain/Stabilized-Space-Time (DSD/SST) formulation. A
difficult issue that is connected with this type of approach is the
determination of a suitable coupling mechanism between the fluid velocity at
the boundary and the displacement of the boundary mesh nodes. In order to avoid
large mesh distortions, one goal is to keep the nodal movements as small as
possible; but of course still compliant with the no-penetration boundary
condition. Standard displacement techniques are full velocity, velocity in a
specific coordinate direction, and velocity in normal direction. In this work,
we investigate how the interface-tracking approach can be combined with
isogeometric analysis for the spatial discretization. If NURBS basis functions
of sufficient order are used for both the geometry and the solution, both a
continuous normal vector as well as the velocity are available on the entire
boundary. This circumstance allows the weak imposition of the no-penetration
boundary condition. We compare this option with an alternative that relies on
strong imposition at discrete points. Furthermore, we examine several coupling
methods between the fluid equations, boundary conditions, and equations for the
adjustment of interior control point positions.Comment: 20 pages, 16 figure
The asymptotic concentration approach combined with isogeometric analysis for topology optimization of two-dimensional linear elasticity structures
We propose an asymptotic concentration approach combined with isogeometric analysis (IGA) for the topology optimization of two-dimensional (2D) linear elasticity structures under the commonly-used framework of the solid isotropic materials and penalty (SIMP) model. Based on the SIMP framework, the B-splines are used as basis functions to describe geometric model in structural finite element analysis, which closely combines geometric modeling with structural analysis. Isogeometric analysis is utilized to define the geometric characteristics of the 2D linear elasticity structures, which can greatly improve the calculation accuracy. In addition, to eliminate the gray-scale intervals usually caused by the intermediate density in the SIMP approach, we utilize the asymptotic concentration method to concentrate the intermediate density values on either 0 or 1 gradually. Consequently, the intermediate densities representing gray-scale intervals in topology optimization results are sufficiently eliminated by virtue of the asymptotic concentration method. The effectiveness and applicability of the proposed method are illustrated by several typical examples
CAD-integrierte Isogeometrische Analyse und Entwurf leichter Tragwerke
Isogeometric methods are extended for the parametric design process of complex lightweight structures. Three novel methods for the coupling of different structural elements are proposed: rotational coupling, implicit geometry description, and frictionless sliding contact. Moreover, the necessary steps for the integration of the numerical analysis, including pre- and post-processing, in CAD are investigated. It is possible to base several different analyses on each other in order to parametrically represent a construction process with multiple steps.Die isogeometrischen Methoden werden zur Anwendung im parametrischen Entwurfsprozess von komplexen Leichtbaustrukturen erweitert. Hierzu werden drei neue Methoden zur Kopplung unterschiedlicher Strukturelemente vorgeschlagen: Rotationskopplung, implizite Geometriebeschreibung und reibungsfreier Gleitkontakt. Ferner werden die nötigen Schritte zur Einbindung von Pre- und Postprocessing für numerische Simulationen in CAD untersucht. Mehrere unterschiedliche Analysen können auf einander folgen und werden verlinkt, um den Aufbauprozess in mehreren Schritten vollparametrisch abzubilden
A framework for isogeometric-analysis-based design and optimization of wind turbine blades
Typical wind turbine blade design procedures employ reduced-order models almost exclusively for early-stage design; high-fidelity, finite-element-based procedures are reserved for later design stages because they entail complex workflows, large volumes of data, and significant computational expense. Yet, high-fidelity structural analyses often provide design-governing feedback such as buckling load factors. Mitigation of the issues of workflow complexity, data volume, and computational expense would allow designers to utilize high-fidelity structural analysis feedback earlier, more easily, and more often in the design process. Thus, this work presents a blade analysis framework which employs isogeometric analysis (IGA), a simulation method that overcomes many of the aforementioned drawbacks associated with traditional finite element analysis (FEA). IGA directly utilizes the mathematical models generated by computer-aided design (CAD) software, requires less user interaction and no conversion of CAD geometries to finite element meshes, and tends to have superior per-degree-of-freedom accuracy compared to traditional FEA.
The presented framework employs the parametric capabilities of the Grasshopper algorithmic modeling interface developed for the CAD software Rhinoceros 3D. This Grasshopper-based framework enables seamless, iterative design and IGA of CAD-based geometries and is demonstrated through the optimization of both a pressurized tube and a simplified wind turbine blade design. Further, because engineering models, such as wind turbine blades, are typically composed of numerous surface patches, a novel patch coupling technique is presented. For the sake of straightforward implementation and flexibility, the coupling technique is based on a penalty energy approach. Formulations for the penalty parameters are proposed to eliminate the problem-dependent nature of the penalty method. This coupling methodology is successfully demonstrated using a number of multi-patch benchmark examples with both matching and non-matching interface discretizations.
Together, these technologies enable practical and efficient design and analysis of wind turbine blade shell structures. The presented IGA approach is employed to perform vibration, buckling, and nonlinear deformation analysis of the NREL/SNL 5 MW wind turbine blade, validating the effectiveness of the proposed approach for realistic, composite wind turbine blade designs. Further, a blade design framework that combines reduced-order aeroelastic analysis with the presented IGA methodologies is outlined. Aeroelastic analysis is used to efficiently provide dynamic kinematic data for a wide range of wind load cases, while IGA is used to perform high-fidelity buckling analysis. Finally, the value and feasibility of incorporating high-fidelity IGA feedback into optimization is demonstrated through optimization of the NREL/SNL 5 MW wind turbine blade. Alternative structural designs that have improved blade mass and material cost characteristics are identified, and IGA-based buckling analysis is shown to provide design-governing constraint information
Topology Optimization of Structures with High Spatial Definition Considering Minimum Weight and Stress Constraints
Programa Oficial de Doutoramento en EnxeñarÃa Civil . 5011V01[Abstract]
The first formulation of Topology Optimization was proposed in 1988. Since then,
many contributions have been presented with the purpose of improving its efficiency
and extending its applicability. In this thesis, a topology optimization algorithm that
allows to obtain the structure of minimum weight that is able to support different loads
is developed. For this purpose, the requirement that stresses have to be lower than a
maximum value has been considered in its development.
Although the structural topology optimization problem with stress constraints have
been previously formulated with several different approaches, a Damage Constraint
approach is developed in this thesis to incorporate them in a different way. The main
objective of this modification is to reduce the CPU time required in the solution of
the topology optimization problem. This reduction will allow to solve problems with a
higher number of design variables what enables the attainment of solutions with high
spatial definition.
Moreover, two different approaches are used to define the material distribution in the
domain: uniform density per element formulation and material density distribution by
means of isogeometric interpolation. In the first approach the Finite Element Method
(FEM) is used to solve the structural analysis and the relative density in each element
of the mesh is chosen as design variable, while the second one uses the Isogeometric
Analysis (IGA) for solving the structural analysis and the values of the relative density
at a certain number of control points are used as design variables.
On the other hand, the optimization is addressed by using Sequential Linear Programming,
that requires a first order sensitivity analysis. All the sensitivities are
obtained through analytic derivatives by using both, direct differentiation and the adjoint
variable method. Finally, some application examples are solved by means of both
methods (FEM and IGA) in the two-dimensional and three-dimensional space.[Resumen]
La primera formulación de la Optimización Topológica fue propuesta en 1988. Desde
entonces muchas aportaciones se han presentado para mejorar su eficiencia y extender
su aplicabilidad. En esta tesis se desarrolla un algoritmo de optimización topológica
que permita obtener la estructura de mÃnimo peso que sea capaz de soportar diferentes
cargas. Para este propósito se ha considerado en su desarrollo la condición de que las
tensiones sean inferiores a un cierto valor máximo.
Aunque el problema de optimización topológica estructural con restricciones de
tensión se formuló previamente con diferentes enfoques, en esta tesis se desarrolla un
enfoque que considera una restricción de daño para incorporarlas de una forma diferente.
El principal objetivo de esta modificación es reducir el tiempo de computación
requerido en la solución del problema de optimización topológica. Esta reducción permitir
´a resolver problemas con un mayor número de variables de diseño lo que a su vez
permite la obtención de soluciones con alta definición espacial.
Para definir la distribución de material en el dominio se usan dos formulaciones
diferentes: formulación de densidad uniforme por elemento y distribución de material
por medio de una interpolación isogeométrica. El primer planteamiento usa el Método
de los Elementos Finitos (MEF) para resolver el análisis estructural y toma como
variable de diseño el valor de la densidad relativa en cada elemento de la malla, mientras
que el segundo requiere del uso del Análisis Isogeométrico (IGA) para resolver el análisis
estructural y los valores de la densidad relativa en un cierto número de puntos de control
son las variables de diseño.
El problema de optimización se resuelve con las técnicas de Programación Lineal Secuencial
requiriendo ´únicamente el análisis de sensibilidad de primer orden. Todas las
derivadas se calculan por derivación analÃtica haciendo uso de las técnicas de derivación
directa y del método de la variable adjunta. Finalmente, se resuelven algunos ejemplos
de aplicación con ambos métodos (MEF e IGA) en el espacio bidimensional y
tridimensional.[Resumo]
A primeira formulación da Optimización Topolóxica foi proposta en 1988. Desde
entón moitas achegas se presentaron para mellorar a súa eficiencia e estender a súa
aplicabilidade. Nesta tese desenvólvese un algoritmo de optimización topolóxica que
permita obter a estrutura de mÃnimo peso que sexa capaz de soportar diferentes cargas.
Para este propósito considerouse no seu desenvolvemento a condición de que as tensións
sexan inferiores a un certo valor máximo.
AÃnda que o problema de optimización topolóxica estrutural con restricións de
tensi´on formulouse previamente con diferentes enfoques, nesta tese desenvólvese un enfoque
que considera unha restrición de dano para incorporalas dunha forma diferente.
O principal obxectivo desta modificación é reducir o tempo de computación requirido
na solución do problema de optimizaci´on topol´oxica. Esta reduci´on permitir´a resolver
problemas cun maior número de variables de dese˜no o que ´a s´ua vez permite a obtención
de solucións con alta definición espacial.
Para definir a distribución de material no dominio úsanse dúas formulacións diferentes:
formulación de densidade uniforme por elemento e distribución de material por
medio dunha interpolación isoxeométrica. A primeira formulación usa o Método dos
Elementos Finitos (MEF) para resolver a análise estrutural e toma coma variable de
deseño o valor da densidade relativa en cada elemento da malla, mentres que o segundo
require do uso da Análise Isoxeométrica (IGA) para resolver a análise estrutural e os
valores da densidade relativa nun certo número de puntos de control son as variables
de deseño.
O problema de optimización resólvese coas técnicas de Programación Lineal Secuencial
requirindo unicamente a análise de sensibilidade de primeira orde. Todas as
derivadas calcúlanse por derivación analÃtica facendo uso das técnicas de derivación
directa e do método da variable adxunta. Finalmente, resólvense algúns exemplos de
aplicación con ámbolos métodos (MEF e IGA) no espazo bidimensional e tridimensionalMinisterio de EconomÃa y Competitividad; DPI2015-68341-RMinisterio de EconomÃa y Competitividad; RTI2018-093366-B-I00Xunta de Galicia; GRC2014/039Xunta de Galicia; GRC2018/4
Phase-field modeling of brittle fracture with multi-level hp-FEM and the finite cell method
The difficulties in dealing with discontinuities related to a sharp crack are
overcome in the phase-field approach for fracture by modeling the crack as a
diffusive object being described by a continuous field having high gradients.
The discrete crack limit case is approached for a small length-scale parameter
that controls the width of the transition region between the fully broken and
the undamaged phases. From a computational standpoint, this necessitates fine
meshes, at least locally, in order to accurately resolve the phase-field
profile. In the classical approach, phase-field models are computed on a fixed
mesh that is a priori refined in the areas where the crack is expected to
propagate. This on the other hand curbs the convenience of using phase-field
models for unknown crack paths and its ability to handle complex crack
propagation patterns. In this work, we overcome this issue by employing the
multi-level hp-refinement technique that enables a dynamically changing mesh
which in turn allows the refinement to remain local at singularities and high
gradients without problems of hanging nodes. Yet, in case of complex
geometries, mesh generation and in particular local refinement becomes
non-trivial. We address this issue by integrating a two-dimensional phase-field
framework for brittle fracture with the finite cell method (FCM). The FCM based
on high-order finite elements is a non-geometry-conforming discretization
technique wherein the physical domain is embedded into a larger fictitious
domain of simple geometry that can be easily discretized. This facilitates mesh
generation for complex geometries and supports local refinement. Numerical
examples including a comparison to a validation experiment illustrate the
applicability of the multi-level hp-refinement and the FCM in the context of
phase-field simulations
Algebraic level sets for CAD/CAE integration and moving boundary problems
Boundary representation (B-rep) of CAD models obtained from solid modeling kernels are commonly used in design, and analysis applications outside the CAD systems. Boolean operations between interacting B-rep CAD models as well as analysis of such multi-body systems are fundamental operations on B-rep geometries in CAD/CAE applications. However, the boundary representation of B-rep solids is, in general, not a suitable representation for analysis operations which lead to CAD/CAE integration challenges due to the need for conversion from B-rep to volumetric approximations. The major challenges include intermediate mesh generation step, capturing CAD features and associated behavior exactly and recurring point containment queries for point classification as inside/outside the solid. Thus, an ideal analysis technique for CAD/CAE integration that can enable direct analysis operations on B-rep CAD models while overcoming the associated challenges is desirable. ^ Further, numerical surface intersection operations are typically necessary for boolean operations on B-rep geometries during the CAD and CAE phases. However, for non-linear geometries, surface intersection operations are non-trivial and face the challenge of simultaneously satisfying the three goals of accuracy, efficiency and robustness. In the class of problems involving multi-body interactions, often an implicit knowledge of the boolean operation is sufficient and explicit intersection computation may not be needed. Such implicit boolean operations can be performed by point containment queries on B-rep CAD models. However, for complex non-linear B-rep geometries, the point containment queries may involve numerical iterative point projection operations which are expensive. Thus, there is a need for inexpensive, non-iterative techniques to enable such implicit boolean operations on B-rep geometries. ^ Moreover, in analysis problems with evolving boundaries (ormoving boundary problems), interfaces or cracks, blending functions are used to enrich the underlying domain with the known behavior on the enriching entity. The blending functions are typically dependent on the distance from the evolving boundaries. For boundaries defined by free form curves or surfaces, the distance fields have to be constructed numerically. This may require either a polytope approximation to the boundary and/or an iterative solution to determine the exact distance to the boundary. ^ In this work a purely algebraic, and computationally efficient technique is described for constructing signed distance measures from Non-Uniform Rational B-Splines (NURBS) boundaries that retain the geometric exactness of the boundaries while eliminating the need for iterative and non-robust distance calculation. The proposed technique exploits the NURBS geometry and algebraic tools of implicitization. Such a signed distance measure, also referred to as the Algebraic Level Sets, gives a volumetric representation of the B-rep geometry constructed by purely non-iterative algebraic operations on the geometry. This in turn enables both the implicit boolean operations and analysis operations on B-rep geometries in CAD/CAE applications. Algebraic level sets ensure exactness of geometry while eliminating iterative numerical computations. Further, a geometry-based analysis technique that relies on hierarchical partition of unity field compositions (HPFC) theory and its extension to enriched field modeling is presented. The proposed technique enables direct analysis of complex physical problems without meshing, thus, integrating CAD and CAE. The developed techniques are demonstrated by constructing algebraic level sets for complex geometries, geometry-based analysis of B-rep CAD models and a variety of fracture examples culminating in the analysis of steady state heat conduction in a solid with arbitrary shaped three-dimensional cracks. ^ The proposed techniques are lastly applied to investigate the risk of fracture in the ultra low-k (ULK) dies due to copper (Cu) wirebonding process. Maximum damage induced in the interlayer dielectric (ILD) stack during the process steps is proposed as an indicator of the reliability risk. Numerical techniques based on enriched isogeometric approximations are adopted to model damage in the ULK stacks using a cohesive damage description. A damage analysis procedure is proposed to conduct damage accumulation studies during Cu wirebonding process. Analysis is carried out to identify weak interfaces and potential sites for crack nucleation as well as damage nucleation patterns. Further, the critical process condition is identified by analyzing the damage induced during the impact and ultrasonic excitation stages. Also, representative ILD stack designs with varying Cu percentage are compared for risk of fracture
Optimal Design of Functionally Graded Parts
Several additive manufacturing processes are capable of fabricating three-dimensional parts with complex distribution of material composition to achieve desired local properties and functions. This unique advantage could be exploited by developing and implementing methodologies capable of optimizing the distribution of material composition for one-, two-, and three-dimensional parts. This paper is the first effort to review the research works on developing these methods. The underlying components (i.e., building blocks) in all of these methods include the homogenization approach, material representation technique, finite element analysis approach, and the choice of optimization algorithm. The overall performance of each method mainly depends on these components and how they work together. For instance, if a simple one-dimensional analytical equation is used to represent the material composition distribution, the finite element analysis and optimization would be straightforward, but it does not have the versatility of a method which uses an advanced representation technique. In this paper, evolution of these methods is followed; noteworthy homogenization approaches, representation techniques, finite element analysis approaches, and optimization algorithms used/developed in these studies are described; and most powerful design methods are identified, explained, and compared against each other. Also, manufacturing techniques, capable of producing functionally graded materials with complex material distribution, are reviewed; and future research directions are discussed
Topology optimization of nonlinear periodically microstructured materials for tailored homogenized constitutive properties
A topology optimization method is presented for the design of periodic
microstructured materials with prescribed homogenized nonlinear constitutive
properties over finite strain ranges. The mechanical model assumes linear
elastic isotropic materials, geometric nonlinearity at finite strain, and a
quasi-static response. The optimization problem is solved by a nonlinear
programming method and the sensitivities computed via the adjoint method.
Two-dimensional structures identified using this optimization method are
additively manufactured and their uniaxial tensile strain response compared
with the numerically predicted behavior. The optimization approach herein
enables the design and development of lattice-like materials with prescribed
nonlinear effective properties, for use in myriad potential applications,
ranging from stress wave and vibration mitigation to soft robotics
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