Results for “Virtual Element Method” — Page 2

NASA NTRS1992

Finite element nonlinear panel flutter with arbitrary temperatures in supersonic flow

A finite element frequency domain method for predicting nonlinear flutter response of panels with temperature effects is presented. By using the principle of virtual work, the element nonlinear stiffness formulation for a panel under a combined thermal and aerodynamic loads is derived on the bases of von Karman's large deflection plate theory, the first-order piston theory aerodynamics and the quasi-steady thermal stress theory. The system equations of motion can be mathematically separated into two sets of equations and then solved in sequence. The first set of equations yields the panel thermal-aerodynamic equilibrium and the second set of equations of motion leads to the flutter limit-cycle oscillations. Stability and flutter boundaries can also be obtained from the two sets of system equations. Finite element large amplitude limit-cycle flutter results at different uniform temperatures are obtained for a simply supported square panel and are compared with existing Galerkin/time integration and other finite element solutions. Effects of nonuniform temperature distributions, panel length-to-width ratios, and boundary conditions on flutter responses of rectangular and triangular panels are presented.

Xue, David Y.↗

NASA NTRSDate not supplied

Interlaminar R-Curve Effects in Thermoplastic Composites: Experiments and Model Correlations

The interlaminar fracture behavior of thermoplastic composites under Mode-I and Mode-II static loading is investigated in this research. The material system under consideration is a carbon fiber reinforced low melt semi-crystalline resin TC1225 LMPAEK T700G (T700/LMPAEK)†. Characterization experiments were conducted to measure the load-displacement response, peak load, and propagation of delamination from a pre-implanted Kapton® insert. The Mode-I response was characterized using a double cantilever beam (DCB) test according to the ASTM D5528-22 standard. It was observed that the propagation exhibited significant resistance to delamination growth, i.e., an R-Curve effect. The test data indicated that the steady-state fracture toughness, G SS I , was approximately twice the mean initiation fracture toughness, G Ic . The Mode-II response of an end notch flexure (ENF) specimen tested according to the ASTM D7905-19 standard exhibited an unexpected stable behavior upon attaining peak load. Prior to attaining peak load, the Mode-II response exhibited some non-linearity, which may be attributed to nonlinear bulk material response, e.g., hyper-elasticity, viscoelasticity, plasticity, etc., and potentially friction at the load/support rollers and R-Curve effects. Finite element models based on the Cohesive Zone Method (CZM) and the Virtual Crack Closure Technique (VCCT) were used to predict the DCB and ENF specimen responses. DCB analysis results obtained using G SS I predicted propagation consistent with experimental data. However, results obtained with the as characterized G Ic were inaccurate in predicting delamination growth onset and peak load. ENF analysis results obtained with the as-characterized Mode-II fracture toughness, G IIc , were inaccurate in predicting the peak load and propagation. Hence, R-Curve effects were included in both DCB and ENF simulations, which enabled improved predictions. The experimentally determined Mode-I R-Curve was used for the DCB simulations, whereas an R-Curve was derived for Mode-II assuming that the change in compliance of the specimen was associated with crack growth only.

Prabhakar M Rao↗

NASA NTRSDate not supplied

Interlaminar R-Curve Effects in Thermoplastic Composites: Experiments and Model Correlations

The interlaminar fracture behavior of thermoplastic composites under Mode-I and Mode-II static loading is investigated in this research. The material system under consideration is a carbon fiber reinforced low melt semi-crystalline resin TC1225 LMPAEK T700G (T700/LMPAEK)†. Characterization experiments were conducted to measure the load-displacement response, peak load, and propagation of delamination from a pre-implanted Kapton® insert. The Mode-I response was characterized using a double cantilever beam (DCB) test according to the ASTM D5528-22 standard. It was observed that the propagation exhibited significant resistance to delamination growth, i.e., an R-Curve effect. The test data indicated that the steady-state fracture toughness, G SS I , was approximately twice the mean initiation fracture toughness, G Ic . The Mode-II response of an end notch flexure (ENF) specimen tested according to the ASTM D7905-19 standard exhibited an unexpected stable behavior upon attaining peak load. Prior to attaining peak load, the Mode-II response exhibited some non-linearity, which may be attributed to nonlinear bulk material response, e.g., hyper-elasticity, viscoelasticity, plasticity, etc., and potentially friction at the load/support rollers and R-Curve effects. Finite element models based on the Cohesive Zone Method (CZM) and the Virtual Crack Closure Technique (VCCT) were used to predict the DCB and ENF specimen responses. DCB analysis results obtained using G SS I predicted propagation consistent with experimental data. However, results obtained with the as characterized G Ic were inaccurate in predicting delamination growth onset and peak load. ENF analysis results obtained with the as-characterized Mode-II fracture toughness, G IIc , were inaccurate in predicting the peak load and propagation. Hence, R-Curve effects were included in both DCB and ENF simulations, which enabled improved predictions. The experimentally determined Mode-I R-Curve was used for the DCB simulations, whereas an R-Curve was derived for Mode-II assuming that the change in compliance of the specimen was associated with crack growth only.

Prabhakar Rao↗

NASA NTRS2017

Interaction of Delaminations and Matrix Cracks in a CFRP Plate, Part II: Simulation Using an Enriched Shell Finite Element Model

Numerical simulations are presented of a recently developed test which creates multiple delaminations in a CFRP laminate specimen that grow and interact via transverse matrix cracks. A novel shell element enriched with the Floating Node Method, and a damage algorithm based on the Virtual Crack Closure Technique, were used to successfully simulate the tests. Additionally, a 3D high mesh fidelity model based on cohesive zones and continuum damage mechanics was used to simulate the tests and act as a representative of other similar state-of-the-art high mesh fidelity modeling techniques to compare to the enriched shell element. The enriched shell and high mesh fidelity models had similar levels of accuracy and generally matched the experimental data. With runtimes of 36 minutes for the shell model and 55 hours for the high mesh fidelity model, the shell model is 92 times faster than the high- fidelity simulation.

Mark W McElroy↗

NASA NTRS2010

Acoustic Noise Prediction of the Amine Swingbed ISS ExPRESS Rack Payload

Acoustics plays a vital role in maintaining the health, safety, and comfort of crew members aboard the International Space Station (ISS). In order to maintain this livable and workable environment, acoustic requirements have been established to ensure that ISS hardware and payload developers account for the acoustic emissions of their equipment and develop acoustic mitigations as necessary. These requirements are verified by an acoustic emissions test of the integrated hardware. The Amine Swingbed ExPRESS (Expedite the PRocessing of ExperimentS to Space) rack payload creates a unique challenge to the developers in that the payload hardware is transported to the ISS in phases, making an acoustic emissions test on the integrated flight hardware impossible. In addition, the payload incorporates a high back pressure fan and a diaphragm vacuum pump, which are recognized as significant and complex noise sources. In order to accurately predict the acoustic emissions of the integrated payload, the individual acoustic noise sources and paths are first characterized. These characterizations are conducted though a series of acoustic emissions tests on the individual payload components. Secondly, the individual acoustic noise sources and paths are incorporated into a virtual model of the integrated hardware. The virtual model is constructed with the use of hybrid method utilizing the Finite Element Acoustic (FEA) and Statistical Energy Analysis (SEA) techniques, which predict the overall acoustic emissions. Finally, the acoustic model is validated though an acoustic characterization test performed on an acoustically similar mock-up of the flight unit. The results of the validated acoustic model are then used to assess the acoustic emissions of the flight unit and define further acoustic mitigation efforts.

Welsh, David↗

NASA NTRSDate not supplied

Composite Progressive Delamination Analysis of Thin Ply Buckling

The NASA Advanced Composites Project is a multi-year consortium of government, industry and academia to develop and validate technology that will reduce development and certification of advanced composite materials for aircraft structures. One of its tasks is to simulate and predict composite damage progression accurately through high fidelity finite element models. It included a subtask to verify an approach based on the Virtual Crack Closure Technology (VCCT) as well as Floating Node Method (FNM). This paper discusses predicted damage onset and growth in a thin-ply buckling problem. Sensitivity of the simulations to various initial crack length is studied. The compressive load-displacement curves are plotted and the crack growth critical load is predicted. Overall, the crack progression follows simulation benchmarks well. However, the critical-load overshoot phenomenon is observed in both VCCT and FNM, suggesting further investigation may be worth pursuing.

damage progression↗

NASA NTRS2000

Three-Dimensional Effects in the Plate Element Analysis of Stitched Textile Composites

Three-dimensional effects related to the analysis of stitched textile composites are discussed. The method of calculation is based on the virtual crack closure technique (VCCT), and models that model the upper and lower surface of the delamination or debond with two-dimensional (2D) plate elements rather than three-dimensional (3D) solid elements. The major advantages of the plate element modeling technique are a smaller model size and simpler geometric modeling. Details of the modeling of the laminated plate and the stitching are discussed.

Glaessgen, E. H.↗

NASA NTRS2016

In Search of a Time Efficient Approach to Crack and Delamination Growth Predictions in Composites

Analysis benchmarking was used to assess the accuracy and time efficiency of algorithms suitable for automated delamination growth analysis. First, the Floating Node Method (FNM) was introduced and its combination with a simple exponential growth law (Paris Law) and Virtual Crack Closure technique (VCCT) was discussed. Implementation of the method into a user element (UEL) in Abaqus/Standard(Registered TradeMark) was also presented. For the assessment of growth prediction capabilities, an existing benchmark case based on the Double Cantilever Beam (DCB) specimen was briefly summarized. Additionally, the development of new benchmark cases based on the Mixed-Mode Bending (MMB) specimen to assess the growth prediction capabilities under mixed-mode I/II conditions was discussed in detail. A comparison was presented, in which the benchmark cases were used to assess the existing low-cycle fatigue analysis tool in Abaqus/Standard(Registered TradeMark) in comparison to the FNM-VCCT fatigue growth analysis implementation. The low-cycle fatigue analysis tool in Abaqus/Standard(Registered TradeMark) was able to yield results that were in good agreement with the DCB benchmark example. Results for the MMB benchmark cases, however, only captured the trend correctly. The user element (FNM-VCCT) always yielded results that were in excellent agreement with all benchmark cases, at a fraction of the analysis time. The ability to assess the implementation of two methods in one finite element code illustrated the value of establishing benchmark solutions.

Krueger, Ronald↗

NASA NTRSDate not supplied

Recent Advances in Discrete Crack Modeling Applied to Laminated Composites with Emphasis on: Floating Node Method, VCCT and Cohesive Zone Modeling

The present talk will provide an overview of the work performed during the Advanced Composites Project (ACP) on the development, and verification and validation of the Floating Node Method (FNM) as well as the Virtual Crack Closure Technique (VCCT) and cohesive zone modeling (CZM). The FNM is a finite element-based technique to represent crack networks. The complex nature of matrix crack-delamination interactions observed in unidirectional (UD) tape laminates suggests that a methodology such as the FNM method may be required to be able to accurately simulate damage progression in these laminates. Simulating crack onset and growth within the context of the FNM relies on techniques such as VCCT and CZM. The talk is organized to provide, via select examples, an overview of the breadth of the Verification & Validation (V&V) exercises performed during the ACP, and how these challenged the state-of-the art and guided further developments in discrete crack modeling, while helping to establish confidence in the progress made and map the challenges ahead. The performance of the VCCT and CZM individually, and in combination with the FNM can be assessed through verification exercises. These exercises typically consist of a comparison of simulation results to known numerical or analytical solutions. Verification is key to identify implementation issues and limitations that, otherwise, may remain undetected and cloud any subsequent validation efforts. Indeed, a subset of these numerical exercises led to further developments of the VCCT and the FNM method as will be illustrated. Before embarking on the subsequent validation of the framework, it is critical to have adequate characterization data. However, the testing campaign conducted revealed material responses that challenged the state-of-the-art and required further developments. The developments in CZM technology associated with the modeling of the responses of hybrid interfaces (fabric/UD) will be given as an example. Finally, the talk will conclude with a summary of the validation exercises performed under quasi-static and fatigue loadings, highlighting some of the key achievements, outstanding challenges and lessons learned.

finite elements↗

NASA NTRS2002

Dynamic Stability of Uncertain Laminated Beams Under Subtangential Loads

Because of the inherent complexity of fiber-reinforced laminated composites, it can be challenging to manufacture composite structures according to their exact design specifications, resulting in unwanted material and geometric uncertainties. In this research, we focus on the deterministic and probabilistic stability analysis of laminated structures subject to subtangential loading, a combination of conservative and nonconservative tangential loads, using the dynamic criterion. Thus a shear-deformable laminated beam element, including warping effects, is derived to study the deterministic and probabilistic response of laminated beams. This twenty-one degrees of freedom element can be used for solving both static and dynamic problems. In the first-order shear deformable model used here we have employed a more accurate method to obtain the transverse shear correction factor. The dynamic version of the principle of virtual work for laminated composites is expressed in its nondimensional form and the element tangent stiffness and mass matrices are obtained using analytical integration The stability is studied by giving the structure a small disturbance about an equilibrium configuration, and observing if the resulting response remains small. In order to study the dynamic behavior by including uncertainties into the problem, three models were developed: Exact Monte Carlo Simulation, Sensitivity Based Monte Carlo Simulation, and Probabilistic FEA. These methods were integrated into the developed finite element analysis. Also, perturbation and sensitivity analysis have been used to study nonconservative problems, as well as to study the stability analysis, using the dynamic criterion.

Goyal, Vijay K.↗

NASA NTRS2015

An Enriched Shell Element for Delamination Simulation in Composite Laminates

A formulation is presented for an enriched shell finite element capable of delamination simulation in composite laminates. The element uses an adaptive splitting approach for damage characterization that allows for straightforward low-fidelity model creation and a numerically efficient solution. The Floating Node Method is used in conjunction with the Virtual Crack Closure Technique to predict delamination growth and represent it discretely at an arbitrary ply interface. The enriched element is verified for Mode I delamination simulation using numerical benchmark data. After determining important mesh configuration guidelines for the vicinity of the delamination front in the model, a good correlation was found between the enriched shell element model results and the benchmark data set.

McElroy, Mark↗

NASA NTRS1988

Strain energy release rate analysis of the end-notched flexure specimen using the finite-element method

Two-dimensional finite-element analysis of the end-notched flexure specimen was performed using 8-node isoparametric, parabolic elements to evaluate compliance and mode II strain energy release rates, G sub II. The G sub II values were computed using two different techniques: the virtual crack-closure technique (VCCT) and the rate of change of compliance with crack length (compliance derivative method). The analysis was performed for various crack-length-to-semi-span (a/L) ratios ranging from 0.2 to 0.9. Three material systems representing a wide range of material properties were analyzed. The compliance and strain energy release rates of the specimen calculated with the present finite-element analysis agree very well with beam theory equations including transverse shear. The G sub II values calculated using the compliance derivative method compared extremely well with those calculated using the VCCT. The G sub II values obtained by the compliance derivative method using the top or bottom beam deflections agreed closely with each other. The strain energy release rates from a plane-stress analysis were higher than the plane-strain values by only a small percentage, indicating that either assumption may be used in the analysis. The G sub II values for one material system calculated from the finte-element analysis agreed with one solution in the literature and disagreed with the other solution in the literature.

Salpekar, S. A.↗

NASA NTRSDate not supplied

A Framework for Optimization-Based ISRU Tool Design Using Discrete Element Modeling

Novel robotic excavation technologies are needed to perform in-situ resource utilization (ISRU) tasks at levels required to sustain a long-term presence on the lunar surface. Developing and testing multiple iterations of functional hardware is time and cost prohibitive, thus slowing down the pace of progress and delaying humanity’s settlement of the Moon. High-fidelity, physics-based simulation can reduce the time and effort required to develop and deploy robotic systems [1]. We have adopted this approach to create high-fidelity models of robotic test hardware to enable rapid virtual design and optimization of excavation technologies [2]. Such models can leverage modern computational tools like Discrete Element Method (DEM) simulations that can be coupled with automated design approaches like topology optimization to reduce the amount of prototyping and physical testing needed to realize useful tools.

ISRU↗

NASA NTRS1996

A General Interface Method for Aeroelastic Analysis of Aircraft

The aeroelastic analysis of an aircraft requires an accurate and efficient procedure to couple aerodynamics and structures. The procedure needs an interface method to bridge the gap between the aerodynamic and structural models in order to transform loads and displacements. Such an interface method is described in this report. This interface method transforms loads computed by any aerodynamic code to a structural finite element (FE) model and converts the displacements from the FE model to the aerodynamic model. The approach is based on FE technology in which virtual work is employed to transform the aerodynamic pressures into FE nodal forces. The displacements at the FE nodes are then converted back to aerodynamic grid points on the aircraft surface through the reciprocal theorem in structural engineering. The method allows both high and crude fidelities of both models and does not require an intermediate modeling. In addition, the method performs the conversion of loads and displacements directly between individual aerodynamic grid point and its corresponding structural finite element and, hence, is very efficient for large aircraft models. This report also describes the application of this aero-structure interface method to a simple wing and an MD-90 wing. The results show that the aeroelastic effect is very important. For the simple wing, both linear and nonlinear approaches are used. In the linear approach, the deformation of the structural model is considered small, and the loads from the deformed aerodynamic model are applied to the original geometry of the structure. In the nonlinear approach, the geometry of the structure and its stiffness matrix are updated in every iteration and the increments of loads from the previous iteration are applied to the new structural geometry in order to compute the displacement increments. Additional studies to apply the aero-structure interaction procedure to more complicated geometry will be conducted in the second phase of the present contract.

Tzong, T.↗

NASA NTRS1993

Non-oscillatory and non-diffusive solution of convection problems by the iteratively reweighted least-squares finite element method

A comparative description is presented for the least-squares FEM (LSFEM) for 2D steady-state pure convection problems. In addition to exhibiting better control of the streamline derivative than the streamline upwinding Petrov-Galerkin method, numerical convergence rates are obtained which show the LSFEM to be virtually optimal. The LSFEM is used as a framework for an iteratively reweighted LSFEM yielding nonoscillatory and nondiffusive solutions for problems with contact discontinuities; this method is shown to convect contact discontinuities without error when using triangular and bilinear elements.

Jiang, Bo-Nan↗

NASA NTRS2002

Formation metrology and control for large separated optics space telescopes

In this paper we present formation flying performance analysis initial results for a representative large space telescope composed of separated optical elements [Mett 02]. A virtual-structure construct (an equivalent rigid body) is created by unique metrology and control that combines both centralized and decentralized methods. The formation may be in orbit at GEO for super-resolution Earth observation, as in the case of Figure 1, or it may be in an Earth-trailing orbit for astrophysics, Figure 2. Extended applications are envisioned for exo-solar planet interferometric imaging by a formation of very large separated optics telescopes, Figure 3. Space telescopes, with such large apertures and f/10 to f/100 optics, are not feasible if connected by massive metering structures. Instead, the new virtual-structure paradigm of information and control connectivity between the formation elements provides the necessary spatial rigidity and alignment precision for the telescope.

formation flying virtual-structure telescopes↗

NASA NTRS1999

Delamination Modeling of Composites for Improved Crash Analysis

Finite element crash modeling of composite structures is limited by the inability of current commercial crash codes to accurately model delamination growth. Efforts are made to implement and assess delamination modeling techniques using a current finite element crash code, MSC/DYTRAN. Three methods are evaluated, including a straightforward method based on monitoring forces in elements or constraints representing an interface; a cohesive fracture model proposed in the literature; and the virtual crack closure technique commonly used in fracture mechanics. Results are compared with dynamic double cantilever beam test data from the literature. Examples show that it is possible to accurately model delamination propagation in this case. However, the computational demands required for accurate solution are great and reliable property data may not be available to support general crash modeling efforts. Additional examples are modeled including an impact-loaded beam, damage initiation in laminated crushing specimens, and a scaled aircraft subfloor structures in which composite sandwich structures are used as energy-absorbing elements. These examples illustrate some of the difficulties in modeling delamination as part of a finite element crash analysis.

Fleming, David C.↗

NASA NTRS1999

Delamination Modeling of Composites for Improved Crash Analysis

Finite element crash modeling of composite structures is limited by the inability of current commercial crash codes to accurately model delamination growth. Efforts are made to implement and assess delamination modeling techniques using a current finite element crash code, MSC/DYTRAN. Three methods are evaluated, including a straightforward method based on monitoring forces in elements or constraints representing an interface; a cohesive fracture model proposed in the literature; and the virtual crack closure technique commonly used in fracture mechanics. Results are compared with dynamic double cantilever beam test data from the literature. Examples show that it is possible to accurately model delamination propagation in this case. However, the computational demands required for accurate solution are great and reliable property data may not be available to support general crash modeling efforts. Additional examples are modeled including an impact-loaded beam, damage initiation in laminated crushing specimens, and a scaled aircraft subfloor structures in which composite sandwich structures are used as energy-absorbing elements. These examples illustrate some of the difficulties in modeling delamination as part of a finite element crash analysis.

Fleming, David C.↗