Total Lagrangian Formulation for Large Deformation Modeling Using Uniform Background Mesh

2016 ◽  
Author(s):  
Nikhil Bhosale ◽  
Ashok V. Kumar
Keyword(s):  
Boundary Conditions ◽  
Large Deformation ◽  
Nonlinear Problems ◽  
Lagrangian Formulation ◽  
Element Analysis ◽  
Static And Dynamic Analysis ◽  
Main Challenge ◽  
Background Mesh ◽  
Uniform Background ◽  
Total Lagrangian Formulation

Mesh generation difficulties can be avoided when a background mesh rather than a mesh that conforms to the geometry is used for the analysis. The geometry is represented by equations and is independent of the mesh and is immersed in the background mesh. The solution to boundary value problems is approximated or piece-wise interpolated using the background mesh. The main challenge is in applying the boundary conditions because the boundaries may not have any nodes on them. Implicit boundary method has been used for linear static and dynamic analysis and has shown to be an effective approach for imposing boundary conditions but has never been applied to nonlinear problems. In this paper, this approach is extended to large deformation nonlinear analysis using the Total Lagrangian formulation. The equations are solved using the widely used modified Newton-Raphson method with loads applied over many load steps. Several test examples are studied and compared with traditional finite element analysis software for verification.

Implicit Boundary Approach for Reissner-Mindlin Plates

2013 ◽  
Author(s):  
Hailong Chen ◽  
Ashok V. Kumar
Keyword(s):  
Boundary Conditions ◽  
Plate Theory ◽  
Weak Form ◽  
Mindlin Plate ◽  
Benchmark Problems ◽  
Element Analysis ◽  
Boundary Method ◽  
Solid Models ◽  
Plate Elements ◽  
Background Mesh

Implicit boundary method enables the use of background mesh to perform finite element analysis while using solid models to represent the geometry. This approach has been used in the past to model 2D and 3D structures. Thin plate or shell-like structures are more challenging to model. In this paper, the implicit boundary method is shown to be effective for plate elements modeled using Reissner-Mindlin plate theory. This plate element uses a mixed formulation and discrete collocation of shear stress field to avoid shear locking. The trial and test functions are constructed by utilizing approximate step functions such that the boundary conditions are guaranteed to be satisfied. The incompatibility of discrete collocation with implicit boundary approach is overcome by using irreducible weak form for computing the stiffness associated with essential boundary conditions. A family of Reissner-Mindlin plate elements is presented and evaluated in this paper using several benchmark problems to test their validity and robustness.

Isoparametric B-Spline Elements for Immersed Boundary Explicit Dynamic Simulation

2020 ◽  
Vol 20 (4) ◽  
Author(s):  
Shashank Menon ◽  
Ashok V. Kumar
Keyword(s):  
Boundary Conditions ◽  
Dynamic Simulation ◽  
Small Time ◽  
Immersed Boundary ◽  
Element Analysis ◽  
B Spline ◽  
B Splines ◽  
Background Mesh ◽  
Definition Of ◽  
Explicit Dynamic

Abstract Explicit dynamic analysis has proven to be advantageous when simulating shock and impact loading, and very small time-scale events. In this article, the feasibility of using a background mesh of B-spline elements for immersed boundary explicit dynamic simulation is studied. In this approach, the geometry is immersed in a background mesh consisting of uniform regular shaped elements to avoid mesh generation difficulties. The boundary conditions are applied using the step boundary method, which uses the equations of the boundaries to construct trial functions that satisfy the essential boundary conditions. An isoparametric formulation is presented for quadratic and cubic B-spline elements and their shape functions are derived from the classical recursive definition of B-splines. The effectiveness of mass diagonalization for B-spline elements is also explored. This approach is validated using several examples by comparing with modal superposition solutions as well as past work using traditional finite element analysis (FEA) and analytical solutions when available.

scholarly journals Shape Sensing of a Complex Aeronautical Structure with Inverse Finite Element Method

Sensors ◽  
2021 ◽  
Vol 21 (4) ◽  
pp. 1388
Author(s):  
Daniele Oboe ◽  
Luca Colombo ◽  
Claudio Sbarufatti ◽  
Marco Giglio
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Boundary Conditions ◽  
Strain Field ◽  
Element Analysis ◽  
Inverse Finite Element Method ◽  
Shape Sensing ◽  
Definition Of ◽  
High Level ◽  
Element Method

The inverse Finite Element Method (iFEM) is receiving more attention for shape sensing due to its independence from the material properties and the external load. However, a proper definition of the model geometry with its boundary conditions is required, together with the acquisition of the structure’s strain field with optimized sensor networks. The iFEM model definition is not trivial in the case of complex structures, in particular, if sensors are not applied on the whole structure allowing just a partial definition of the input strain field. To overcome this issue, this research proposes a simplified iFEM model in which the geometrical complexity is reduced and boundary conditions are tuned with the superimposition of the effects to behave as the real structure. The procedure is assessed for a complex aeronautical structure, where the reference displacement field is first computed in a numerical framework with input strains coming from a direct finite element analysis, confirming the effectiveness of the iFEM based on a simplified geometry. Finally, the model is fed with experimentally acquired strain measurements and the performance of the method is assessed in presence of a high level of uncertainty.

scholarly journals Effects of Loading and Boundary Conditions on the Performance of Ultrasound Compressional Viscoelastography: A Computational Simulation Study to Guide Experimental Design

Materials ◽  
2021 ◽  
Vol 14 (10) ◽  
pp. 2590
Author(s):  
Che-Yu Lin ◽  
Ke-Vin Chang
Keyword(s):  
Boundary Conditions ◽  
Simulation Study ◽  
Viscoelastic Properties ◽  
Measurement Accuracy ◽  
Computational Simulation ◽  
Vertical Direction ◽  
Fixation Method ◽  
Element Analysis ◽  
Sample Container

Most biomaterials and tissues are viscoelastic; thus, evaluating viscoelastic properties is important for numerous biomedical applications. Compressional viscoelastography is an ultrasound imaging technique used for measuring the viscoelastic properties of biomaterials and tissues. It analyzes the creep behavior of a material under an external mechanical compression. The aim of this study is to use finite element analysis to investigate how loading conditions (the distribution of the applied compressional pressure on the surface of the sample) and boundary conditions (the fixation method used to stabilize the sample) can affect the measurement accuracy of compressional viscoelastography. The results show that loading and boundary conditions in computational simulations of compressional viscoelastography can severely affect the measurement accuracy of the viscoelastic properties of materials. The measurement can only be accurate if the compressional pressure is exerted on the entire top surface of the sample, as well as if the bottom of the sample is fixed only along the vertical direction. These findings imply that, in an experimental validation study, the phantom design should take into account that the surface area of the pressure plate must be equal to or larger than that of the top surface of the sample, and the sample should be placed directly on the testing platform without any fixation (such as a sample container). The findings indicate that when applying compressional viscoelastography to real tissues in vivo, consideration should be given to the representative loading and boundary conditions. The findings of the present simulation study will provide a reference for experimental phantom designs regarding loading and boundary conditions, as well as guidance towards validating the experimental results of compressional viscoelastography.

The Finite Element Analysis and Optimization for the Grinder Based on the Joint Surface

2013 ◽  
Vol 281 ◽  
pp. 165-169 ◽  
Author(s):  
Xiang Lei Zhang ◽  
Bin Yao ◽  
Wen Chang Zhao ◽  
Ou Yang Kun ◽  
Bo Shi Yao
Keyword(s):  
Finite Element ◽  
Natural Frequency ◽  
Element Model ◽  
Joint Surface ◽  
Weak Links ◽  
Response Analysis ◽  
Element Analysis ◽  
Static And Dynamic Analysis ◽  
Harmonic Response Analysis ◽  
Grinding Machine

Establish the finite element model for high precision grinding machine which takes joint surface into consideration and then carrys out the static and dynamic analysis of the grinder. After the static analysis, modal analysis and harmonic response analysis, the displacement deformation, stress, natural frequency and vibration mode could be found, which also helps find the weak links out. The improvement scheme which aims to increase the stiffness and precision of the whole machine has proposed to efficiently optimize the grinder. And the first natural frequency of the optimized grinder has increased by 68.19%.

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