Modal analysis of elastic vibrations of incompressible materials using a pressure-stabilized finite element method

Codina, Ramon; Türk, Önder

doi:10.1016/j.finel.2022.103760

Cited by 6 publications

(5 citation statements)

References 44 publications

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“…In recent years, cloth simulation has seen significant advancements, including techniques such as finite element methods [25], which divide the cloth into small elements and solve equations of motion for each element. More sophisticated models that incorporate both stretching and bending stiffness have also been explored for more realistic simulations of cloth behavior [26], [27].…”

Section: Methodsmentioning

confidence: 99%

Coefficient Prediction for Physically-based Cloth Simulation Using Deep learning

Mao,

Va,

Hong

2023

Int. J. Adv. Sci. Eng. Inf. Technol.

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Physically-based cloth simulation involves modeling cloth as a collection of particles or nodes connected by various types of constraints. These particles interact with each other and the environment, such as gravity or collisions, to accurately simulate the cloth's behavior. One essential component of such simulations is the set of material parameters or coefficients that dictate the cloth's physical properties, such as stiffness and damping. Deep learning-based coefficient prediction in physically-based cloth simulation involves using machine learning techniques, specifically deep neural networks, to predict the material parameters of cloth from its geometric and physical properties. The deep learning model is trained using a dataset of simulated cloth instances, where the material parameters are known. The input to the model is a set of geometric and physical properties of the cloth, such as the dimensions, orientation, and velocity. The output of the model is the set of material parameters that best represent the cloth's behavior under these conditions. This paper proposes a deep learning method for predicting these coefficients using a multi-label video classification approach. The training data is generated from a physics-based simulator, and the method is evaluated on some cloth simulations, such as fabric falling down, fabric with collision, and fabric affected by airflow. The cloth movement dataset is generated from a mass-spring-based simulation. The results show that the transformer model has much higher accuracy than other models. This study provides a promising approach for predicting the coefficients of virtual cloth in physically-based simulations.

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Section: Methodsmentioning

confidence: 99%

Coefficient Prediction for Physically-based Cloth Simulation Using Deep learning

Mao,

Va,

Hong

2023

Int. J. Adv. Sci. Eng. Inf. Technol.

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“…The governing equations must be supplied with initial conditions of the form u = u 0 , 𝜕u 𝜕t = v 0 in Ω 0 at t = 0, with u 0 and v 0 given, and a set of boundary conditions which can be split into Dirichlet boundary conditions (22), where the displacement is prescribed, or Neumann boundary conditions (23), where the value of tractions t N are prescribed, that is…”

Section: Governing Equationsmentioning

confidence: 99%

“…The variational statement of the problem is derived by testing system ( 19)-( 21) against arbitrary test functions, V := [v, q, T] T , v ∈ V 0 , q ∈ Q and T ∈ T. The weak form of the problem reads: find U := [u, p, S ] T : ]0, T [ → W such that initial conditions and the Dirichlet condition (22) are satisfied and…”

Section: 4mentioning

confidence: 99%

“…The analysis and FE approximation of Darcy's problem presented in [18] motivated the introduction of both strains/displacements and stresses/displacements pairs as primary variables in [19] for infinitesimal strain elasticity; in this particular case, one can change the functional framework to increase the accuracy in the calculation of the stresses. To tackle the incompressible limit, the pressure needs to be introduced as a variable [20,21,22], although it is also possible to design a formulation using the volumetric strain as unknown [23]. Formulations including stresses as unknowns produce a considerable increase in the number of unknowns per node, but they also increase the accuracy for strains and stresses.…”

Section: Introductionmentioning

confidence: 99%

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A stabilized mixed three‐field formulation for stress accurate analysis including the incompressible limit in finite strain solid dynamics

Castañar

Codina

Baiges

2023

Numerical Meth Engineering

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In this work a new methodology for finite strain solid dynamics problems for stress accurate analysis including the incompressible limit is presented.In previous works, the authors have presented the stabilized mixed displacement/pressure formulation to deal with the incompressibility constraint in finite strain solid dynamics. To this end, the momentum equation is complemented with a constitutive law for the pressure which emerges from the deviatoric/volumetric decomposition of the strain energy function for any hyperelastic material model. The incompressible limit is attained automatically depending on the material bulk modulus. This work exploits the concept of mixed methods to formulate stable displacement/pressure/deviatoric stress finite elements. The final goal is to design a finite element technology able to tackle simultaneously problems which may involve incompressible behavior together with a high degree of accuracy of the stress field. The variational multi-scale stabilization technique and, in particular, the orthogonal subgrid scale method allows the use of equal-order interpolations. These stabilization procedures lead to discrete problems which are fully stable, free of volumetric locking, stress oscillations and pressure fluctuations. Numerical benchmarks show that the results obtained compare very favorably with those obtained with the corresponding stabilized mixed displacement/pressure formulation.

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“…Modal analysis is mainly used to analyze the vibration characteristics of the structure; the natural frequency and vibration mode are determined according to factors such as the structure and material [20,21], providing the basis for subsequent analysis. Let the thickness and radius distributions of the flexural vibration disk have the proportions ( ) a h a .…”

Section: Modal Analysismentioning

confidence: 99%

Simulation and Optimization of Piezoelectric Micromachined Ultrasonic Transducer Unit Based on AlN

Ren

Wan

et al. 2022

Electronics

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The relatively low piezoelectric constant of aluminum nitride (AlN) piezoelectric film limits the development and application of the acoustic field performance of AlN-based micromachined ultrasonic transducers; thus, in this study we establish a mid- to low-frequency transducer unit model to address this problem. The transducer operates at 4.5 MHz, and the construction of a clamped structure is first investigated to ensure the feasibility of performance analysis. Secondly, the effectiveness of the optimized upper electrode distribution proposed in this paper in improving the acoustic field radiation of the array element is also compared with the original structure. Finally, the influence of the optimized electrode geometry parameters on the acoustic wave direction is analyzed. The finite element simulations are performed in the COMSOL Multiphysics (COMSOL) software and post-processing results are analyzed. Based on the simulation results, the proposed optimal distribution of the upper electrode makes the radiation beam uniform and symmetrical in the case of both the clamped model and the optimized structure model. In the case of the upper electrode radius of 28 µm, this electrode division operation makes the unit vibration mode switching in the frequency range more moderate. The sound field radiation improvement of the proposed optimized structure model is better than that of the clamped structure.

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Modal analysis of elastic vibrations of incompressible materials using a pressure-stabilized finite element method

Cited by 6 publications

References 44 publications

Coefficient Prediction for Physically-based Cloth Simulation Using Deep learning

Coefficient Prediction for Physically-based Cloth Simulation Using Deep learning

A stabilized mixed three‐field formulation for stress accurate analysis including the incompressible limit in finite strain solid dynamics

Simulation and Optimization of Piezoelectric Micromachined Ultrasonic Transducer Unit Based on AlN

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