Geometrically Nonlinear Response of Beam and Membrane Structures by Exact Reduction Technique

1998 ◽  
Author(s):  
Cho W. S. To ◽  
Lingchuan Li
Keyword(s):  
Finite Element ◽  
Nonlinear Response ◽  
Large Scale ◽  
Computational Cost ◽  
Free Vibration Analysis ◽  
Structural Systems ◽  
Second Phase ◽  
Geometrically Nonlinear ◽  
Theoretic Approach ◽  
Membrane Structures

Abstract Large scale dynamic finite element analysis of complex nonlinear mechanical or structural systems can be very expensive. To significantly reduce the computational cost various techniques have been developed and presented in the literature. The reduction method based on symmetry group or the so-called group theoretic approach (GTA) of Healey and associates for bifurcation analysis and free vibration analysis of geometrically nonlinear systems with symmetries has been extended by the authors to deal with transient geometrically nonlinear response of structures discretized by the finite element method (FEM). Computed results for two discretized space trusses were obtained with the GTA, and presented by the authors in a previous paper. Application is further made of the GTA for the computation of geometrically nonlinear response of beam and membrane structures during the second phase of the investigation reported here. The obtained numerical results indicate that the GTA can be applied to relatively more complicated structural systems that include symmetry of nodal rotations. It was observed that the results obtained by the GTA are very accurate and the GTA is very efficient compared with technique for the full space problems.

scholarly journals Prediction of Residual Stresses in a Multipass Pipe Weld by a Novel 3D Finite Element Approach

2018 ◽  
Author(s):  
Hui Huang ◽  
Jian Chen ◽  
Blair Carlson ◽  
Hui-Ping Wang ◽  
Paul Crooker ◽  
...  
Keyword(s):  
Finite Element ◽  
Residual Stresses ◽  
High Performance ◽  
Large Scale ◽  
Graphics Processing Unit ◽  
Computational Cost ◽  
Three Dimensional ◽  
Processing Unit ◽  
Girth Welds ◽  
Welding Processes

Due to enormous computation cost, current residual stress simulation of multipass girth welds are mostly performed using two-dimensional (2D) axisymmetric models. The 2D model can only provide limited estimation on the residual stresses by assuming its axisymmetric distribution. In this study, a highly efficient thermal-mechanical finite element code for three dimensional (3D) model has been developed based on high performance Graphics Processing Unit (GPU) computers. Our code is further accelerated by considering the unique physics associated with welding processes that are characterized by steep temperature gradient and a moving arc heat source. It is capable of modeling large-scale welding problems that cannot be easily handled by the existing commercial simulation tools. To demonstrate the accuracy and efficiency, our code was compared with a commercial software by simulating a 3D multi-pass girth weld model with over 1 million elements. Our code achieved comparable solution accuracy with respect to the commercial one but with over 100 times saving on computational cost. Moreover, the three-dimensional analysis demonstrated more realistic stress distribution that is not axisymmetric in hoop direction.

Process modeling, joint-property characterization and construction of joint connectors for mechanical fastening by self-piercing riveting

2014 ◽  
Vol 10 (4) ◽  
pp. 631-658 ◽  
Author(s):  
Mica Grujicic ◽  
Jennifer Snipes ◽  
S. Ramaswami ◽  
Fadi Abu-Farha
Keyword(s):  
Mechanical Properties ◽  
Finite Element ◽  
Large Scale ◽  
Constitutive Relations ◽  
Computational Cost ◽  
Three Dimensional ◽  
Modeling And Simulations ◽  
Content Type ◽  
Material Parameters ◽  
Computational Analyses

Purpose – The purpose of this paper is to propose a computational approach in order to help establish the effect of various self-piercing rivet (SPR) process and material parameters on the quality and the mechanical performance of the resulting SPR joints. Design/methodology/approach – Toward that end, a sequence of three distinct computational analyses is developed. These analyses include: (a) finite-element modeling and simulations of the SPR process; (b) determination of the mechanical properties of the resulting SPR joints through the use of three-dimensional, continuum finite-element-based numerical simulations of various mechanical tests performed on the SPR joints; and (c) determination, parameterization and validation of the constitutive relations for the simplified SPR connectors, using the results obtained in (b) and the available experimental results. The availability of such connectors is mandatory in large-scale computational analyses of whole-vehicle crash or even in simulations of vehicle component manufacturing, e.g. car-body electro-coat paint-baking process. In such simulations, explicit three-dimensional representation of all SPR joints is associated with a prohibitive computational cost. Findings – It is found that the approach developed in the present work can be used, within an engineering optimization procedure, to adjust the SPR process and material parameters (design variables) in order to obtain a desired combination of the SPR-joint mechanical properties (objective function). Originality/value – To the authors’ knowledge, the present work is the first public-domain report of the comprehensive modeling and simulations including: self-piercing process; virtual mechanical testing of the SPR joints; and derivation of the constitutive relations for the SPR connector elements.

Semi-Implicit Coupling of CS-FEM and FEM for the Interaction Between a Geometrically Nonlinear Solid and an Incompressible Fluid

2015 ◽  
Vol 12 (05) ◽  
pp. 1550025 ◽  
Author(s):  
Tao He
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Incompressible Fluid ◽  
Computational Cost ◽  
Geometrically Nonlinear ◽  
Arbitrary Lagrangian Eulerian ◽  
Coupling Strategy ◽  
Smoothed Finite Element Method ◽  
Characteristic Based Split ◽  
Element Method

A semi-implicit coupling strategy under the arbitrary Lagrangian–Eulerian description is presented for the incompressible fluid flow past a geometrically nonlinear solid in this paper. The incompressible fluid is solved by means of the characteristic-based split (CBS) finite element method while the cell-based smoothed finite element method is employed to settle the governing equation of the geometrically nonlinear solid. Because of the CBS fluid solver, the present coupling strategy is performed in a semi-implicit fashion. In particular, the first step of the CBS scheme is explicitly treated whereas the others are implicitly coupled with the structural motion. The computational cost is hence reduced because no subiterations are included in the explicit coupling step and the fluid mesh is frozen in the implicit coupling step. A classic cantilever problem is dealt with to validate the structural solver, and then flow-induced vibrations of a restrictor flap in a uniform channel flow is analyzed in detail. The obtained results agree well with the existing data.

Efficient Uncertainty Quantification in Structural Dynamic Analysis Using Two-Level Gaussian Processes

2015 ◽  
Author(s):  
Kai Zhou ◽  
Pei Cao ◽  
Jiong Tang
Keyword(s):  
Finite Element ◽  
Dynamic Analysis ◽  
Uncertainty Quantification ◽  
Large Scale ◽  
Computational Cost ◽  
Response Prediction ◽  
Element Model ◽  
High Fidelity ◽  
Structural Dynamic ◽  
Rapid Sampling

Uncertainty quantification is an important aspect in structural dynamic analysis. Since practical structures are complex and oftentimes need to be characterized by large-scale finite element models, component mode synthesis (CMS) method is widely adopted for order-reduced modeling. Even with the model order-reduction, the computational cost for uncertainty quantification can still be prohibitive. In this research, we utilize a two-level Gaussian process emulation to achieve rapid sampling and response prediction under uncertainty, in which the low- and high-fidelity data extracted from CMS and full-scale finite element model are incorporated in an integral manner. The possible bias of low-fidelity data is then corrected through high-fidelity data. For the purpose of reducing the emulation runs, we further employ Bayesian inference approach to calibrate the order-reduced model in a probabilistic manner conditioned on multiple predicted response distributions of concern. Case studies are carried out to validate the effectiveness of proposed methodology.

A Computationally Efficient Finite Element Framework to Simulate Additive Manufacturing Processes

2018 ◽  
Vol 140 (4) ◽  
Author(s):  
Shiyan Jayanath ◽  
Ajit Achuthan
Keyword(s):  
Finite Element ◽  
Additive Manufacturing ◽  
Large Scale ◽  
Computational Cost ◽  
Cylindrical Part ◽  
Adaptive Meshing ◽  
Computationally Efficient ◽  
Thin Walled ◽  
Melt Pool Size ◽  
Simulation Time

Macroscale finite element (FE) models, with their ability to simulate additive manufacturing (AM) processes of metal parts and accurately predict residual stress distribution, are potentially powerful design tools. However, these simulations require enormous computational cost, even for a small part only a few orders larger than the melt pool size. The existing adaptive meshing techniques to reduce computational cost substantially by selectively coarsening are not well suited for AM process simulations due to the continuous modification of model geometry as material is added to the system. To address this limitation, a new FE framework is developed. The new FE framework is based on introducing updated discretized geometries at regular intervals during the simulation process, allowing greater flexibility to control the degree of mesh coarsening than a technique based on element merging recently reported in the literature. The new framework is evaluated by simulating direct metal deposition (DMD) of a thin-walled rectangular and a thin-walled cylindrical part, and comparing the computational speed and predicted results with those predicted by simulations using the conventional framework. The comparison shows excellent agreement in the predicted stress and plastic strain fields, with substantial savings in the simulation time. The method is then validated by comparing the predicted residual elastic strain with that measured experimentally by neutron diffraction of the thin-walled rectangular part. Finally, the new framework's capability to substantially reduce the simulation time for large-scale AM parts is demonstrated by simulating a one-half foot thin-walled cylindrical part.

A FINITE ELEMENT-BASED PERTURBATION METHOD FOR NONLINEAR FREE VIBRATION ANALYSIS OF COMPOSITE CYLINDRICAL SHELLS

2011 ◽  
Vol 11 (04) ◽  
pp. 717-734 ◽  
Author(s):  
T. RAHMAN ◽  
E. L. JANSEN ◽  
P. TISO
Keyword(s):  
Finite Element ◽  
Perturbation Method ◽  
Nonlinear Vibration ◽  
Vibration Analysis ◽  
Cylindrical Shells ◽  
Computational Cost ◽  
Free Vibration Analysis ◽  
Perturbation Approach ◽  
Frequency Relation ◽  
Composite Cylindrical Shells

In this paper, a finite element-based approach for nonlinear vibration analysis of shell structures is presented. The approach makes use of a perturbation method that gives an approximation for the amplitude-frequency relation of the structure. The method is formulated using a functional notation and is subsequently converted to a finite element notation. After the determination of the linear natural frequency and corresponding vibration mode, the perturbation approach yields the initial curvature of the amplitude–frequency relation with a modest additional computational cost. The implementation of the perturbation approach in a general purpose finite element code using a laminated curved shell element is described. The effectiveness of the approach is illustrated by application to single-mode and coupled-mode nonlinear vibration analyses of cylindrical shells. Results for isotropic and composite cylindrical shells are presented and compared with results obtained via alternative approaches.

Exact Reduction by Group Theoretic Approach in Computational Nonlinear Structural Dynamics

1997 ◽  
Author(s):  
Cho W. S. To ◽  
Lingchuan Li
Keyword(s):  
Nonlinear Systems ◽  
Free Vibration Analysis ◽  
Response Analysis ◽  
Geometrically Nonlinear ◽  
Theoretic Approach ◽  
Central Difference ◽  
Central Difference Method ◽  
Fortran Language ◽  
Reduced Space ◽  
Space Trusses

Abstract The reduction method based on symmetry group or the so-called group theoretic approach (GTA) of Healey and associates for bifurcation analysis and free vibration analysis of geometrically nonlinear systems with symmetries is applied in the investigation reported here to the computations of responses of geometrically nonlinear systems under intensive transient excitations. A digital computer program written in Fortran language has also been developed for the work. Two space trusses discretized by the finite element method are chosen to illustrate the use of the GTA for cases undergoing large deflections. In the response computations for both the full space and reduced space or subspace problems the central difference method is employed. Numerical results are obtained. Comparisons of results for full space problems to subspace problems are made. It is concluded that the GTA is mathematically very elegant and rigorous. Computationally, the solution is exact and it is very efficient for geometrically nonlinear systems undergoing large deformation. The GTA is currently being developed for the response analysis of geometrically nonlinear systems with partial symmetries.

Process modeling, joint virtual testing and construction of joint connectors for mechanical fastening by flow-drilling screws

2015 ◽  
Vol 231 (6) ◽  
pp. 1048-1061 ◽  
Author(s):  
Mica Grujicic ◽  
JS Snipes ◽  
S Ramaswami
Keyword(s):  
Mechanical Properties ◽  
Finite Element ◽  
Large Scale ◽  
Mechanical Performance ◽  
Constitutive Relations ◽  
Computational Cost ◽  
Three Dimensional ◽  
Material Parameters ◽  
Computational Analyses ◽  
Flow Drilling

In this work, a computational approach is proposed in order to help establish the effect of various flow-drilling screw process and material parameters on the quality and the mechanical performance of the resulting flow-drilling screw joints. Toward that end, a sequence of three distinct computational analyses is developed. These analyses include the following: (a) finite element modeling and simulations of the flow-drilling screw process; (b) determination of the mechanical properties of the resulting flow-drilling screw joints through the use of three-dimensional, continuum finite element–based numerical simulations of various mechanical tests performed on the flow-drilling screw joints and (c) determination, parameterization and validation of the constitutive relations for the simplified flow-drilling screw connectors, using the results obtained in (b) and the available experimental results. The availability of such connectors is mandatory in large-scale computational analyses of whole-vehicle crash or even in simulations of vehicle component manufacturing, for example, car-body electro-coat paint-baking process. In such simulations, explicit three-dimensional representation of all flow-drilling screw joints is associated with a prohibitive computational cost. The approach developed in this work can be used, within an engineering-optimization procedure, to adjust the flow-drilling screw process and material parameters (design variables) in order to obtain a desired combination of the flow-drilling screw joint mechanical properties (objective function).

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