Engineering PapersSearch

SEARCH · Engineering Papers

Results for “Virtual element method”

Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

Quote a phrase for an exact phrase match. Source license links do not imply unrestricted reuse.

At least 109 records · Page 6

Modified Mode-I Cracked Sandwich Beam (CSB) Fracture Test

Five composite sandwich panels were fabricated using vacuum assisted resin transfer molding (VARTM). Four of these panels had E-glass/vinylester facesheets and one had carbon/epoxy facesheets. The sandwich panels had different density PVC foam cores. The four E-glass panels had core densities of 80, 100, 130, 200 kg/cu m. The sandwich with carbon/epoxy 3 facesheets had a core with density of 100 kg/cu m. Fracture tests were conducted using a modified Cracked Sandwich Beam (CSB) test configuration. Load displacement curves were obtained for loading and unloading of the specimens during crack growth. Various increments of crack growth were monitored. Critical Strain Energy Release Rates (SERR) were determined from the tests using the area method. The critical values of SERR can be considered the fracture toughness of the sandwich material. The fracture toughness ranged 367 J/sq m to 1350 J/sq m over the range of core densities. These results are compared to the Mode-I fracture toughness of the PVC foam core materials and values obtained for foam-cored sandwiches using the TSD specimen. Finite-element analyses (FEA) were performed for the test configuration and Strain Energy Release Rates were calculated using the Virtual Crack Closure Technique (VCCT). The SERR values determined from the FEA were scaled to the fracture loads, or critical loads, obtained from the modified CSB tests. These critical loads were in close agreement with the test values.

Smith, S. A.

Exploration Medical Capability IMPACT Medical Database – Medical Item Database (MedID) Content Development Methods

The Informing Mission Planning via Analysis of Complex Tradespaces (IMPACT) project encompasses a suite of computational tools that are used to inform systematic trade study evaluations and research prioritizations regarding the optimization of spaceflight medical systems, including the provision of risk assessment metrics, for a given design reference mission (DRM). The IMPACT Medical Database (IMPACT-MD) is the component that virtually houses the clinical and engineering data for medical conditions, capabilities, and resources used to support these analyses. In addition, IMPACT-MD also provides data to the associated SysML model to support the Level 2, Level 3, and Level 4 requirements development needed for IMPACT. IMPACT-MD contains an internal Evidence Library (EL) sub-component that hosts the clinical evidence, treatment and outcome metric data, and incidence data for each medical condition identified for exploration-class missions. Furthermore, a separate Medical Item Database (MedID) sub-component hosts the engineering data and physical attributes (e.g., mass, volume, power, etc.) associated with each medical resource item identified to address the requisite medical conditions. The IMPACT project is conducted under the Exploration Medical Capability (ExMC) element of the Human Research Program (HRP) within NASA's Space Operations Mission Directorate (SOMD). The reader is referred to the documents in Appendix A for a more complete overview of the IMPACT tool suite and functionality as well as further detail on any associated aspects of the project. The primary purpose of this document is to describe the methods utilized in the collection and verification of engineering data content during the project development phase for the MedID sub-component of the IMPACT-MD project. Engineering content data (both existing and new/future) will be stored in IMPACT-MD for use by the IMPACT project. This document will detail the content development and data credibility for the engineering data housed within the MedID subcomponent of IMPACT-MD, which is used to inform the IMPACT 1.0 project deliverables.

Exploration Medical Capability

A Method for Calculating Strain Energy Release Rates in Preliminary Design of Composite Skin/Stringer Debonding Under Multi-Axial Loading

Three simple procedures were developed to determine strain energy release rates, G, in composite skin/stringer specimens for various combinations of unaxial and biaxial (in-plane/out-of-plane) loading conditions. These procedures may be used for parametric design studies in such a way that only a few finite element computations will be necessary for a study of many load combinations. The results were compared with mixed mode strain energy release rates calculated directly from nonlinear two-dimensional plane-strain finite element analyses using the virtual crack closure technique. The first procedure involved solving three unknown parameters needed to determine the energy release rates. Good agreement was obtained when the external loads were used in the expression derived. This superposition technique was only applicable if the structure exhibits a linear load/deflection behavior. Consequently, a second technique was derived which was applicable in the case of nonlinear load/deformation behavior. The technique involved calculating six unknown parameters from a set of six simultaneous linear equations with data from six nonlinear analyses to determine the energy release rates. This procedure was not time efficient, and hence, less appealing. A third procedure was developed to calculate mixed mode energy release rates as a function of delamination lengths. This procedure required only one nonlinear finite element analysis of the specimen with a single delamination length to obtain a reference solution for the energy release rates and the scale factors. The delamination was extended in three separate linear models of the local area in the vicinity of the delamination subjected to unit loads to obtain the distribution of G with delamination lengths. This set of sub-problems was Although additional modeling effort is required to create the sub- models, this local technique is efficient for parametric studies.

Krueger, Ronald

Correlated Electromagnetic Levitation Actuator: A Reaction Sphere Based Attitude Control System

To address problems experienced by current reaction wheels and control moment gyroscopebased attitude control systems (ACS), researchers at NASA’s Marshall Space Flight Center have begun developing a reaction sphere actuator based on correlated electromagnetic levitation that will be immune to destructive bearing friction, momentum saturation, and gimbal lock. The Correlated Electromagnetic Levitation Actuator (CELA) advances the state of the art of reaction sphere ACSs by employing the concept of correlated magnetics. It is a frictionless, direct-drive reaction sphere that harnesses a unique technology with an array of applications across multiple disciplines. Correlated electromagnets function in a manner that is analogous to a matched filter; the convolution of two signals is peaked at the index representing the greatest match. For CELA, the signals are the patterns of magnetic flux density as a function of position. The magnitude of the convolution equates to an attractive or repulsive force, and these forces can be azimuthal or radial. The development of CELA is based in four distinct disciplines: Advanced Manufacturing, Prototype Development, Electromagnetic Modeling, and Controls. We are developing novel manufacturing techniques required to build arrays of permanent and electromagnet dipoles on curved surfaces. To print the permanent magnetic array, we have developed a probe with pyramidal magnets that will reside on a robotic arm to induce localized magnetic fields on a surface. The probe also includes the ability to erase dipole patterns from a permanent magnet by heating the surface to its Curie temperature. A number of test articles and prototypes have been developed using additive manufacturing methods. These prototypes have included hemispherical motors to test the drive algorithm, and a levitation test bed that demonstrates a magnetic bearing method based on attractive magnetic forces and ratiometric Hall effect sensors. We developed an array of electromagnetic dipoles on a printed circuit board (PCB) with individual H-bridges controlling each coil. This device created various flux density patterns and we measured their magnetic fields using a custom Hall effect 3-D probe and a LabVIEW virtual instrument. These data will serve as a benchmark for characterizing the accuracy of future models. Current work is focused on modeling the magnetic fields of our prototype arrays using COMSOL Finite Element Analysis and verifying the model against our test data. Accurate modeling will allow us to quickly test new patterns of electromagnets and their macro behavior. Eventually, the magnetic field models will be implemented in our controls simulations to facilitate precise control of the reaction sphere. Initial model results agree with field measurements to within 1 G (5% of measured flux density). Currently, we are testing different material properties of the electromagnets and their magnetic fields and thermal effects. These results will be used to refine the design of the electromagnetic dipoles. Our control efforts have centered on developing commutation, levitation, and field pattern shaping hardware in the form of breadboards and PCBs with software running on a local microcontroller. In addition, our partners developed MATLAB Simulink models to demonstrate a PID controller thatmitigates disturbance forces resulting from the interaction of drive and levitation magnetics. Finally, we have designed a three-axis test stand that will be used in future work to demonstrate CELA’s orientation control capability.

controls

Correlated Electromagnetic Levitation Actuator: A Reaction Sphere-Based Attitude Control System

To address problems experienced by current reaction wheels and control moment gyroscopebased attitude control systems (ACS), researchers at National Aeronautics and Space Administration’s (NASA’s) Marshall Space Flight Center (MSFC) have begun developing a reaction sphere actuator based on correlated electromagnetic levitation that will be immune to destructive bearing friction, momentum saturation, and gimbal lock. The Correlated Electromagnetic Levitation Actuator (CELA) advances the state of the art of reaction sphere ACSs by employing the concept of correlated magnetics. It is a frictionless, direct-drive reaction sphere that harnesses a unique technology with an array of applications across multiple disciplines. Correlated electromagnets function in a manner that is analogous to a matched filter; the convolution of two signals is peaked at the index representing the greatest match. For CELA, the signals are the patterns of magnetic flux density as a function of position. The magnitude of the convolution equates to an attractive or repulsive force, and these forces can be azimuthal or radial. The development of CELA is based in four distinct disciplines: Advanced Manufacturing, Prototype Development, Electromagnetic Modeling, and Controls. We are developing novel manufacturing techniques required to build arrays of permanent and electromagnet dipoles on curved surfaces. To print the permanent magnetic array, we have developed a probe with pyramidal magnets that will reside on a robotic arm to induce localized magnetic fields on a surface. We have also used high temperature ovens to erase dipole patterns from a permanent magnet by heating the surface to its Curie temperature. A number of test articles and prototypes have been developed using additive manufacturing methods. These prototypes have included hemispherical motors to test the drive algorithm, and a levitation test bed that demonstrates a magnetic bearing method based on attractive magnetic forces and ratiometric Hall effect sensors. We developed an array of electromagnetic dipoles on a printed circuit board (PCB) with individual H-bridges controlling each coil. This device created various flux density patterns and we measured their magnetic fields using a custom Hall effect 3-D probe and a LabVIEW virtual instrument. These data will serve as a benchmark for characterizing the accuracy of future models. Current work is focused on modeling the magnetic fields of our prototype arrays using COMSOL finite element analysis (FEA) and verifying the model against our test data. Accurate modeling will allow us to quickly test new patterns of electromagnets and their macro behavior. Eventually, the magnetic field models will be implemented in our controls simulations to facilitate precise control of the reaction sphere. Initial model results agree with field measurements to within 1 G (5% of measured flux density). Currently, we are testing different material properties of the electromagnets and their magnetic fields and thermal effects. These results will be used to refine the design of the electromagnetic dipoles. Our control efforts have centered on developing commutation, levitation, and field pattern shaping hardware in the form of breadboards and PCBs with software running on a local microcontroller. In addition, our partners developed MATLAB Simulink models to demonstrate a PID controller that mitigates disturbance forces resulting from the interaction of drive and levitation magnetics. Finally, we have designed a three-axis test stand that will be used in future work to demonstrate CELA’s orientation control capability.

reaction sphere

Nonlinear Analysis of Bonded Composite Tubular Lap Joints

The present study describes a semi-analytical solution method for predicting the geometrically nonlinear response of a bonded composite tubular single-lap joint subjected to general loading conditions. The transverse shear and normal stresses in the adhesive as well as membrane stress resultants and bending moments in the adherends are determined using this method. The method utilizes the principle of virtual work in conjunction with nonlinear thin-shell theory to model the adherends and a cylindrical shear lag model to represent the kinematics of the thin adhesive layer between the adherends. The kinematic boundary conditions are imposed by employing the Lagrange multiplier method. In the solution procedure, the displacement components for the tubular joint are approximated in terms of non-periodic and periodic B-Spline functions in the longitudinal and circumferential directions, respectively. The approach presented herein represents a rapid-solution alternative to the finite element method. The solution method was validated by comparison against a previously considered tubular single-lap joint. The steep variation of both peeling and shearing stresses near the adhesive edges was successfully captured. The applicability of the present method was also demonstrated by considering tubular bonded lap-joints subjected to pure bending and torsion.

E. Oterkus

Hierarchic plate and shell models based on p-extension

Formulation of hierarchic sequences of finite element models for beams, arches, plates and shells based on the principle of virtual work is described. The exact solutions corresponding to models in the hierarchic sequence converge to the exact solution of the fully three-dimensional problem of linear elasticity. The stopping criterion is that the functionals of interest must be substantially independent of the choice of the model. This process is closely related to p-extensions. Aspects of implementation are discussed in connection with axisymmetric shells and an example is presented. An application of superconvergent extraction methods for the computation of stress resultants is demonstrated.

Szabo, B. A.

Navier-Stokes calculations for unsteady three-dimensional vortical flows in unbounded domains

Finite-difference Navier-Stokes calculations for unsteady, three-dimensional, incompressible, viscous flows induced by initial vorticity distributions are presented and discussed in this paper. The initial vorticity distributions are assumed to be embedded in a flow field of infinite extent that is quiescent at infinity. These vorticity distributions are typical of vortex rings and other closed vortical tubes or structures. Such structures are important elements in fluid flows such as jets, atmospheric convection and the far-field wakes of aircraft; studies of their interaction may aid in an understanding of complex fluid flows. The calculations employ a method recently proposed by Ting to approximate the infinite-domain boundary value problem with a finite boundary computational domain, and this method is shown to yield accurate three-dimensional results for reasonable expenditures of computer time. Because of the efficiency of the boundary condition technique and the resulting Navier-Stokes code, a 16-bit minicomputer with virtual memory was capable of performing the calculations for the unsteady motion of two obliquely colliding vortex rings. The results of these calculations are presented in the paper.

Chamberlain, J. P.

Vibratory tactile display for textures

We have developed a tactile display that produces vibratory stimulus to a fingertip in contact with a vibrating tactor matrix. The display depicts tactile surface textures while the user is exploring a virtual object surface. A piezoelectric actuator drives the individual tactor in accordance with both the finger movement and the surface texture being traced. Spatiotemporal display control schemes were examined for presenting the fundamental surface texture elements. The temporal duration of vibratory stimulus was experimentally optimized to simulate the adaptation process of cutaneous sensation. The selected duration time for presenting a single line edge agreed with the time threshold of tactile sensation. Then spatial stimulus disposition schemes were discussed for representation of other edge shapes. As an alternative means not relying on amplitude control, a method of augmented duration at the edge was investigated. Spatial resolution of the display was measured for the lines presented both in perpendicular and parallel to a finger axis. Discrimination of texture density was also measured on random dot textures.

Ikei, Yasushi

Plasticity Tool for Predicting Shear Nonlinearity of Unidirectional Laminates Under Multiaxial Loading

This study implements a plasticity tool to predict the nonlinear shear behavior of unidirectional composite laminates under multiaxial loadings, with an intent to further develop the tool for use in composite progressive damage analysis. The steps for developing the plasticity tool include establishing a general quadratic yield function, deriving the incremental elasto-plastic stress-strain relations using the yield function with associated flow rule, and integrating the elasto-plastic stress-strain relations with a modified Euler method and a substepping scheme. Micromechanics analyses are performed to obtain normal and shear stress-strain curves that are used in determining the plasticity parameters of the yield function. By analyzing a micromechanics model, a virtual testing approach is used to replace costly experimental tests for obtaining stress-strain responses of composites under various loadings. The predicted elastic moduli and Poisson's ratios are in good agreement with experimental data. The substepping scheme for integrating the elasto-plastic stress-strain relations is suitable for working with displacement-based finite element codes. An illustration problem is solved to show that the plasticity tool can predict the nonlinear shear behavior for a unidirectional laminate subjected to multiaxial loadings.

Wang, John T.

Phase compatibilities of YBa2Cu3O(9-delta) type structure in quintenary systems Y-Ba-Cu-O-X (impurity)

Electrical transport properties of the oxidic high T(sub c) superconductors are significantly affected by the presence of minor amounts of various elements adventing as impurities, e.g., from the chemical environment during manufacturing. YBa2Cu3O(9-delta) is prone to an extinction of the superconductivity on (partial) substitution of all four elemental components. E.g., Pr (for Y), La (for Ba), Zn (for Cu) or peroxygroup (for O) substituents will alter some of the superconductivity preconditions, like mixed valence state in Cu3O7/O(9-delta) network or structural distortion of the network. Although various pseudoternary chemical equilibrium phase diagrams of the Y(O)-Ba(O)-Cu(O) system now are available, no consensus is generally shown, however, this is partly due to lack of compatible definitions of the equilibrium conditions. Less information is available about the phase compatibilities in the appropriate quaternary phase diagram (including oxygen) and virtually no information exists about any pentenary phase diagrams (including one impurity). Unfortunately, complexity of such systems, stemming both from number of quaternary or pentenary compounds and from visualizing the five-component phase system, limits this presentation to more or less close surroundings of the YBa2Cu3O(9-delta) type phase in appropriate pseudoquaternary or pseudopseudoternary diagrams, involving Y-Ba-Cu and O, O-CO2, alkaline metals, Mg and alkaline earths, and Sc and most of the 3-d and 4-f elements. The systems were investigated by means of x ray diffraction, neutron diffraction and chemical analytical methods on samples prepared by sol-gel technique from citrates. The superconductivity was characterized by measuring the diamagnetic susceptibility by SQUID.

Karen, P.

The Heliophysics Data Environment, Virtual Observatories, NSSDC, and SPASE

Heliophysics (the study of the Sun and its effects on the Solar System, especially the Earth) has an interesting data environment in that the data are often to be found in relatively small data sets widely scattered in archives around the world. Within the last decade there have been more concentrated efforts to organize the data access methods and create a Heliophysics Data and Model Consortium (HDMC). To provide data search and access capability a number of Virtual Observatories (VO's) have been established both via funding from the U.S. National Aeronautics and Space Administration (NASA) and through other funding agencies in the U.S. and worldwide. At least 15 systems can be labeled as Heliophysics Virtual Observatories, 9 of them funded by NASA. Other parts of this data environment include Resident Archives, and the final, or "deep" archive at the National Space Science Data Center (NSSDC). The problem is that different data search and access approaches are used by all of these elements of the HDMC and a search for data relevant to a particular research question can involve consulting with multiple VO's - needing to learn a different approach for finding and acquiring data for each. The Space Physics Archive Search and Extract (SPASE) project is intended to provide a common data model for Heliophysics data and therefore a common set of metadata for searches of the VO's and other data environment elements. The SPASE Data Model has been developed through the common efforts of the HDMC representatives over a number of years. We currently have released Version 2.1. of the Data Model. The advantages and disadvantages of the Data Model will be discussed along with the plans for the future. Recent changes requested by new members of the SPASE community indicate some of the directions for further development.

Thieman, James

Fault Mitigation Schemes for Future Spaceflight Multicore Processors

Future planetary exploration missions demand significant advances in on-board computing capabilities over current avionics architectures based on a single-core processing element. The state-of-the-art multi-core processor provides much promise in meeting such challenges while introducing new fault tolerance problems when applied to space missions. Software-based schemes are being presented in this paper that can achieve system-level fault mitigation beyond that provided by radiation-hard-by-design (RHBD). For mission and time critical applications such as the Terrain Relative Navigation (TRN) for planetary or small body navigation, and landing, a range of fault tolerance methods can be adapted by the application. The software methods being investigated include Error Correction Code (ECC) for data packet routing between cores, virtual network routing, Triple Modular Redundancy (TMR), and Algorithm-Based Fault Tolerance (ABFT). A robust fault tolerance framework that provides fail-operational behavior under hard real-time constraints and graceful degradation will be demonstrated using TRN executing on a commercial Tilera(R) processor with simulated fault injections.

software based

A Technique for Mapping Characteristic Lengths to Preserve Energy Dissipated via Strain Softening in a Multiscale Analysis

It is often advantageous to account for the microstructure of the material directly using multiscale modeling. For computational tractability, an idealized repeating unit cell (RUC) is used to capture all of the pertinent features of the microstructure. Typically, the RUC is dimensionless and depends only on the relative volume fractions of the different phases in the material. This works well for non-linear and inelastic behavior exhibiting a positive-definite constitutive response. Although, once the material exhibits strain softening, or localization, a mesh objective failure theories, such as smeared fracture theories, nodal and element enrichment theories (XFEM), cohesive elements or virtual crack closure technique (VCCT), can be utilized at the microscale, but the dimensions of the RUC must then be defined. One major challenge in multiscale progressive damage modeling is relating the characteristic lengths across the scales in order to preserve the energy that is dissipated via localization at the microscale. If there is no effort to relate the size of the macroscale element to the microscale RUC, then the energy that is dissipated will remain mesh dependent at the macroscale, even if it is regularized at the microscale. Here, a technique for mapping characteristic lengths across the scales is proposed. The RUC will be modeled using the generalized method of cells (GMC) micromechanics theory, and local failure in the matrix constituent subcells will be modeled using the crack band theory. The subcell characteristic lengths used in the crack band calculations will be mapped to the macroscale finite element in order to regularize the local energy in a manner consistent with the global length scale. Examples will be provided with and without the regularization, and they will be compared to a baseline case where the size and shape of the element and RUC are coincident (ensuring energy is preserved across the scales).

softening

Implementation of equivalent domain integral method in the two-dimensional analysis of mixed mode problems

An equivalent domain integral (EDI) method for calculating J-intergrals for two-dimensional cracked elastic bodies is presented. The details of the method and its implementation are presented for isoparametric elements. The total and product integrals consist of the sum of an area of domain integral and line integrals on the crack faces. The line integrals vanish only when the crack faces are traction free and the loading is either pure mode 1 or pure mode 2 or a combination of both with only the square-root singular term in the stress field. The EDI method gave accurate values of the J-integrals for two mode I and two mixed mode problems. Numerical studies showed that domains consisting of one layer of elements are sufficient to obtain accurate J-integral values. Two procedures for separating the individual modes from the domain integrals are presented. The procedure that uses the symmetric and antisymmetric components of the stress and displacement fields to calculate the individual modes gave accurate values of the integrals for all problems analyzed. The EDI method when applied to a problem of an interface crack in two different materials showed that the mode 1 and mode 2 components are domain dependent while the total integral is not. This behavior is caused by the presence of the oscillatory part of the singularity in bimaterial crack problems. The EDI method, thus, shows behavior similar to the virtual crack closure method for bimaterial problems.

Raju, I. S.

NASA Tech Briefs, April 2011

Topics covered include: Amperometric Solid Electrolyte Oxygen Microsensors with Easy Batch Fabrication; Two-Axis Direct Fluid Shear Stress Sensor for Aerodynamic Applications; Target Assembly to Check Boresight Alignment of Active Sensors; Virtual Sensor Test Instrumentation; Evaluation of the Reflection Coefficient of Microstrip Elements for Reflectarray Antennas; Miniaturized Ka-Band Dual-Channel Radar; Continuous-Integration Laser Energy Lidar Monitor; Miniaturized Airborne Imaging Central Server System; Radiation-Tolerant, SpaceWire-Compatible Switching Fabric; Small Microprocessor for ASIC or FPGA Implementation; Source-Coupled, N-Channel, JFET-Based Digital Logic Gate Structure Using Resistive Level Shifters; High-Voltage-Input Level Translator Using Standard CMOS; Monitoring Digital Closed-Loop Feedback Systems; MASCOT - MATLAB Stability and Control Toolbox; MIRO Continuum Calibration for Asteroid Mode; GOATS Image Projection Component; Coded Modulation in C and MATLAB; Low-Dead-Volume Inlet for Vacuum Chamber; Thermal Control Method for High-Current Wire Bundles by Injecting a Thermally Conductive Filler; Method for Selective Cleaning of Mold Release from Composite Honeycomb Surfaces; Infrared-Bolometer Arrays with Reflective Backshorts; Commercialization of LARC (trade mark) -SI Polyimide Technology; Novel Low-Density Ablators Containing Hyperbranched Poly(azomethine)s; Carbon Nanotubes on Titanium Substrates for Stray Light Suppression; Monolithic, High-Speed Fiber-Optic Switching Array for Lidar; Grid-Tied Photovoltaic Power System; Spectroelectrochemical Instrument Measures TOC; A Miniaturized Video System for Monitoring Drosophila Behavior; Hydrofocusing Bioreactor Produces Anti-Cancer Alkaloids; Creep Measurement Video Extensometer; Radius of Curvature Measurement of Large Optics Using Interferometry and Laser Tracker n-B-pi-p Superlattice Infrared Detector; Safe Onboard Guidance and Control Under Probabilistic Uncertainty; General Tool for Evaluating High-Contrast Coronagraphic Telescope Performance Error Budgets; Hidden Statistics of Schroedinger Equation; Optimal Padding for the Two-Dimensional Fast Fourier Transform; Spatial Query for Planetary Data; Higher Order Mode Coupling in Feed Waveguide of a Planar Slot Array Antenna; Evolutionary Computational Methods for Identifying Emergent Behavior in Autonomous Systems; Sampling Theorem in Terms of the Bandwidth and Sampling Interval; Meteoroid/Orbital Debris Shield Engineering Development Practice and Procedure; Self-Balancing, Optical-Center-Pivot, Fast-Steering Mirror; Wireless Orbiter Hang-Angle Inclinometer System; and Internal Electrostatic Discharge Monitor - IESDM.

Source record

Nonlinear Analysis of Bonded Composite Single-LAP Joints

This study presents a semi-analytical solution method to analyze the geometrically nonlinear response of bonded composite single-lap joints with tapered adherend edges under uniaxial tension. The solution method provides the transverse shear and normal stresses in the adhesive and in-plane stress resultants and bending moments in the adherends. The method utilizes the principle of virtual work in conjunction with von Karman s nonlinear plate theory to model the adherends and the shear lag model to represent the kinematics of the thin adhesive layer between the adherends. Furthermore, the method accounts for the bilinear elastic material behavior of the adhesive while maintaining a linear stress-strain relationship in the adherends. In order to account for the stiffness changes due to thickness variation of the adherends along the tapered edges, their in-plane and bending stiffness matrices are varied as a function of thickness along the tapered region. The combination of these complexities results in a system of nonlinear governing equilibrium equations. This approach represents a computationally efficient alternative to finite element method. Comparisons are made with corresponding results obtained from finite-element analysis. The results confirm the validity of the solution method. The numerical results present the effects of taper angle, adherend overlap length, and the bilinear adhesive material on the stress fields in the adherends, as well as the adhesive, of a single-lap joint

Oterkus, E.

Separation of crack extension modes in orthotropic delamination models

In the analysis of an interface crack between dissimilar elastic materials, the mode of crack extension is typically not unique, due to oscillatory behavior of near-tip stresses and displacements. This behavior currently limits the applicability of interfacial fracture mechanics as a means to predict composite delamination. The Virtual Crack Closure Technique (VCCT) is a method used to extract mode 1 and mode 2 energy release rates from numerical fracture solutions. The mode of crack extension extracted from an oscillatory solution using the VCCT is not unique due to the dependence of mode on the virtual crack extension length, Delta. In this work, a method is presented for using the VCCT to extract Delta-independent crack extension modes for the case of an interface crack between two in-plane orthotropic materials. The method does not involve altering the analysis to eliminate its oscillatory behavior. Instead, it is argued that physically reasonable, Delta-independent modes of crack extension can be extracted from oscillatory solutions. Knowledge of near-tip fields is used to determine the explicit Delta dependence of energy release rate parameters. Energy release rates are then defined that are separated from the oscillatory dependence on Delta. A modified VCCT using these energy release rate definitions is applied to results from finite element analyses, showing that Delta-independent modes of crack extension result. The modified technique has potential as a consistent method for extracting crack extension modes from numerical solutions. The Delta-independent modes extracted using this technique can also serve as guides for testing the convergence of finite element models. Direct applications of this work include the analysis of planar composite delamination problems, where plies or debonded laminates are modeled as in-plane orthotropic materials.

Beuth, Jack L.