287 research outputs found
Isogeometric iFEM analysis of thin shell structures
Shape sensing is one of most crucial components of typical structural health monitoring systems and has become a promising technology for future large-scale engineering structures to achieve significant improvement in their safety, reliability, and affordability. The inverse finite element method (iFEM) is an innovative shape-sensing technique that was introduced to perform three-dimensional displacement reconstruction of structures using in situ surface strain measurements. Moreover, isogeometric analysis (IGA) presents smooth function spaces such as non-uniform rational basis splines (NURBS), to numerically solve a number of engineering problems, and recently received a great deal of attention from both academy and industry. In this study, we propose a novel “isogeometric iFEM approach” for the shape sensing of thin and curved shell structures, through coupling the NURBS-based IGA together with the iFEM methodology. The main aim is to represent exact computational geometry, simplify mesh refinement, use smooth basis/shape functions, and allocate a lower number of strain sensors for shape sensing. For numerical implementation, a rotation-free isogeometric inverse-shell element (isogeometric Kirchhoff–Love inverse-shell element (iKLS)) is developed by utilizing the kinematics of the Kirchhoff–Love shell theory in convected curvilinear coordinates. Therefore, the isogeometric iFEM methodology presented herein minimizes a weighted-least-squares functional that uses membrane and bending section strains, consistent with the classical shell theory. Various validation and demonstration cases are presented, including Scordelis–Lo roof, pinched hemisphere, and partly clamped hyperbolic paraboloid. Finally, the effect of sensor locations, number of sensors, and the discretization of the geometry on solution accuracy is examined and the high accuracy and practical aspects of isogeometric iFEM analysis for linear/nonlinear shape sensing of curved shells are clearly demonstrated
The multiplicative deformation split for shells with application to growth, chemical swelling, thermoelasticity, viscoelasticity and elastoplasticity
This work presents a general unified theory for coupled nonlinear elastic and
inelastic deformations of curved thin shells. The coupling is based on a
multiplicative decomposition of the surface deformation gradient. The
kinematics of this decomposition is examined in detail. In particular, the
dependency of various kinematical quantities, such as area change and
curvature, on the elastic and inelastic strains is discussed. This is essential
for the development of general constitutive models. In order to fully explore
the coupling between elastic and different inelastic deformations, the surface
balance laws for mass, momentum, energy and entropy are examined in the context
of the multiplicative decomposition. Based on the second law of thermodynamics,
the general constitutive relations are then derived. Two cases are considered:
Independent inelastic strains, and inelastic strains that are functions of
temperature and concentration. The constitutive relations are illustrated by
several nonlinear examples on growth, chemical swelling, thermoelasticity,
viscoelasticity and elastoplasticity of shells. The formulation is fully
expressed in curvilinear coordinates leading to compact and elegant expressions
for the kinematics, balance laws and constitutive relations
A new anisotropic bending model for nonlinear shells: Comparison with existing models and isogeometric finite element implementation
A new nonlinear hyperelastic bending model for shells formulated directly in
surface form is presented, and compared to four prominently used bending
models. Through an essential set of elementary nonlinear bending test cases,
the stresses and moments of each model are examined analytically. Only the
proposed bending model passes all the test cases while the other bending models
either fail or only pass the test cases for small deformations. The proposed
new bending model can handle large deformations and initially curved surfaces.
It is based on the principal curvatures and their directions in the initial
configuration, and it thus can have different bending moduli along those
directions. These characteristics make it flexible in modeling a given
material, while it does not suffer from the pathologies of existing bending
models. Further, the bending models are compared computationally through four
classical benchmark examples and one contact example. As the underlying shell
theory is based on Kirchhoff-Love kinematics, isogeometric NURBS shape
functions are used to discretize the shell surface. The linearization and
efficient finite element implementation of the proposed new model are also
provided
Kirchhoff-Love shell representation and analysis using triangle configuration B-splines
This paper presents the application of triangle configuration B-splines
(TCB-splines) for representing and analyzing the Kirchhoff-Love shell in the
context of isogeometric analysis (IGA). The Kirchhoff-Love shell formulation
requires global -continuous basis functions. The nonuniform rational
B-spline (NURBS)-based IGA has been extensively used for developing
Kirchhoff-Love shell elements. However, shells with complex geometries
inevitably need multiple patches and trimming techniques, where stitching
patches with high continuity is a challenge. On the other hand, due to their
unstructured nature, TCB-splines can accommodate general polygonal domains,
have local refinement, and are flexible to model complex geometries with
continuity, which naturally fit into the Kirchhoff-Love shell formulation with
complex geometries. Therefore, we propose to use TCB-splines as basis functions
for geometric representation and solution approximation. We apply our method to
both linear and nonlinear benchmark shell problems, where the accuracy and
robustness are validated. The applicability of the proposed approach to shell
analysis is further exemplified by performing geometrically nonlinear
Kirchhoff-Love shell simulations of a pipe junction and a front bumper
represented by a single patch of TCB-splines
Use of interpolation methods for modeling the stress-strain state of operated oil storage tanks
The aim of the research is the comparison of two approaches for computer modeling of the stress-strain state of thin-walled shells of engineering structures, considering the imperfections of the geometric shapes arising due to their operation. The object of the study is the operated steel vertical cylindrical reservoir with imperfections of the geometric shape intended for storage of petroleum products. The first, so-called classical, approach provides geometric modeling of the surface of the tank's shell with the subsequent import of the geometric model into one of the systems of finite element analysis to calculate the stress-strain state of the structure and determine its technical condition, and the possibility of further operation. The geometric modeling of the shell surface with imperfections was performed using a two-dimensional interpolation method based on the 1st order smoothness outlines implemented in the point calculus. The calculation of the stress-strain state of the shell was carried out in the SCAD Office computer complex, taking into account geometric and structural non-linearity on the basis of the octahedral tangential stress theory. The second approach assumes modeling of an array of functions of vertical deflection of the tank wall by means of interpolation, solution of an array of differential equations of the elastic cylindrical shell under axisymmetric loading, improved by introduction of vertical deflection functions of the wall, followed by two-dimensional interpolation and analysis of the deformed state of the shell based on displacements arising in the tank wall from the hydrostatic load. As a result of the effective use of two-dimensional interpolation in the process of implementing the second approach, it was possible to achieve a significant increase in the speed of the numerical solution while maintaining sufficient accuracy for engineering calculations
SOLID-SHELL FINITE ELEMENT MODELS FOR EXPLICIT SIMULATIONS OF CRACK PROPAGATION IN THIN STRUCTURES
Crack propagation in thin shell structures due to cutting is conveniently simulated
using explicit finite element approaches, in view of the high nonlinearity of the problem. Solidshell
elements are usually preferred for the discretization in the presence of complex material
behavior and degradation phenomena such as delamination, since they allow for a correct
representation of the thickness geometry. However, in solid-shell elements the small thickness
leads to a very high maximum eigenfrequency, which imply very small stable time-steps. A new
selective mass scaling technique is proposed to increase the time-step size without affecting
accuracy. New ”directional” cohesive interface elements are used in conjunction with selective
mass scaling to account for the interaction with a sharp blade in cutting processes of thin ductile
shells
NeuralClothSim: Neural Deformation Fields Meet the Kirchhoff-Love Thin Shell Theory
Cloth simulation is an extensively studied problem, with a plethora of
solutions available in computer graphics literature. Existing cloth simulators
produce realistic cloth deformations that obey different types of boundary
conditions. Nevertheless, their operational principle remains limited in
several ways: They operate on explicit surface representations with a fixed
spatial resolution, perform a series of discretised updates (which bounds their
temporal resolution), and require comparably large amounts of storage.
Moreover, back-propagating gradients through the existing solvers is often not
straightforward, which poses additional challenges when integrating them into
modern neural architectures. In response to the limitations mentioned above,
this paper takes a fundamentally different perspective on physically-plausible
cloth simulation and re-thinks this long-standing problem: We propose
NeuralClothSim, i.e., a new cloth simulation approach using thin shells, in
which surface evolution is encoded in neural network weights. Our
memory-efficient and differentiable solver operates on a new continuous
coordinate-based representation of dynamic surfaces, i.e., neural deformation
fields (NDFs); it supervises NDF evolution with the rules of the non-linear
Kirchhoff-Love shell theory. NDFs are adaptive in the sense that they 1)
allocate their capacity to the deformation details as the latter arise during
the cloth evolution and 2) allow surface state queries at arbitrary spatial and
temporal resolutions without retraining. We show how to train our
NeuralClothSim solver while imposing hard boundary conditions and demonstrate
multiple applications, such as material interpolation and simulation editing.
The experimental results highlight the effectiveness of our formulation and its
potential impact.Comment: 27 pages, 22 figures and 3 tables; project page:
https://4dqv.mpi-inf.mpg.de/NeuralClothSim
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