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At least 505 records · Page 28

New integration techniques for chemical kinetic rate equations. II - Accuracy comparison

A comparison of the accuracy of several techniques recently developed for solving stiff differential equations is presented. The techniques examined include two general purpose codes EEPISODE and LSODE developed for an arbitrary system of ordinary differential equations, and three specialized codes CHEMEQ, CREKID, and GCKP84 developed specifically to solve chemical kinetic rate equations. The accuracy comparisons are made by applying these solution procedures to two practical combustion kinetics problems. Both problems describe adiabatic, homogeneous, gas phase chemical reactions at constant pressure, and include all three combustion regimes: induction heat release, and equilibration. The comparisons show that LSODE is the most efficient code - in the sense that it requires the least computational work to attain a specified accuracy level. An important finding is that an iterative solution of the algebraic enthalpy conservation equation for the temperature can be more accurate and efficient than computing the temperature by integrating its time derivative.

Radhakrishnan, K.↗

Finite element (MARC) solution technologies for viscoplastic analyses

A need for development of realistic constitutive models for structural components operating at high temperatures, accompanied by appropriate solution technologies for stress/life analyses of these components is studied. Viscoplastic models provide a better description of inelastic behavior of materials, but their mathematical structure is very complex. The highly nonlinear and stiff nature of the constitutive equations makes analytical solutions difficult. Therefore, suitable solution, finite element or other numerical, technologies must be developed to make these models adaptable for better and rational designs of components. NASA-Lewis has developed several solution technologies and successfully applied them to the solution of a number of uniaxial and multiaxial problems. Some of these solution technologies are described along with the models and representative results. The solution technologies developed and presented encompass a wide range of models, such as, isotropic, anisotropic, metal matrix composites, and single crystal models.

Arya, V. K.↗

Polymer/Silicate Nanocomposites Used to Manufacture Gas Storage Tanks With Reduced Permeability

Over the past decade, there has been considerable research in the area of polymer-layered silicate nanocomposites. This research has shown that the dispersion of small amounts of an organically modified layered silicate improves the polymer strength, modulus, thermal stability, and barrier properties. There have been several reports on the dispersion of layered silicates in an epoxy matrix. Potential enhancements to the barrier properties of epoxy/silicate nanocomposites make this material attractive for low permeability tankage. Polymer matrix composites (PMCs) have several advantages for cryogenic storage tanks. They are lightweight, strong, and stiff; therefore, a smaller fraction of a vehicle's potential payload capacity is used for propellant storage. Unfortunately, the resins typically used to make PMC tanks have higher gas permeability than metals. This can lead to hydrogen loss through the body of the tank instead of just at welds and fittings. One approach to eliminate this problem is to build composite tanks with thin metal liners. However, although these tanks provide good permeability performance, they suffer from a substantial mismatch in the coefficient of thermal expansion, which can lead to failure of the bond between the liner and the body of the tank. Both problems could be addressed with polymersilicate nanocomposites, which exhibit reduced hydrogen permeability, making them potential candidates for linerless PMC tanks. Through collaboration with Northrop Grumman and Michigan State University, nanocomposite test tanks were manufactured for the NASA Glenn Research Center, and the helium permeability was measured. An organically modified silicate was prepared at Michigan State University and dispersed in an epoxy matrix (EPON 826/JeffamineD230). The epoxy/silicate nanocomposites contained either 0 or 5 wt% of the organically modified silicate. The tanks were made by filament winding carbon fibers with the nanocomposite resin. Helium permeability was measured by Northrop Grumman, showing that the leak rate/day of the nanocomposite matrix tank was approximately 80-percent less than that of the neat epoxy matrix tank.

Campbell, Sandi G.↗

Improved isoparametric solid and membrane elements

Improvements that were made to the COSMIC NASTRAN elements CIHEX1 and QDMEM1 are described. These elements are isoparametric representations of solid and membrane elastic behavior. Recent papers by the authors have shown the official COSMIC versions of these elements to be inferior to those available in the MacNeal-Schwendler Corporation (MSC) version of NASTRAN in that they are overly stiff for some loadings. Modifications were made to these elements which reduce the order of integration for shear terms and, for the eight-mode solid element, add additional strain functions. The resulting element formulations give behavior similar to that of the MSC elements. The changes made in the element formulations are discussed and results of test problems are compared with results from the official COSMIC elements and with the MSC elements.

Case, W. R.↗

Design of bearings for rotor systems based on stability

Design of rotor systems incorporating stable behavior is of great importance to manufacturers of high speed centrifugal machinery since destabilizing mechanisms (from bearings, seals, aerodynamic cross coupling, noncolocation effects from magnetic bearings, etc.) increase with machine efficiency and power density. A new method of designing bearing parameters (stiffness and damping coefficients or coefficients of the controller transfer function) is proposed, based on a numerical search in the parameter space. The feedback control law is based on a decentralized low order controller structure, and the various design requirements are specified as constraints in the specification and parameter spaces. An algorithm is proposed for solving the problem as a sequence of constrained 'minimax' problems, with more and more eigenvalues into an acceptable region in the complex plane. The algorithm uses the method of feasible directions to solve the nonlinear constrained minimization problem at each stage. This methodology emphasizes the designer's interaction with the algorithm to generate acceptable designs by relaxing various constraints and changing initial guesses interactively. A design oriented user interface is proposed to facilitate the interaction.

Dhar, D.↗

Modeling of composite beams and plates for static and dynamic analysis

A rigorous theory and the corresponding computational algorithms were developed for through-the-thickness analysis of composite plates. This type of analysis is needed in order to find the elastic stiffness constants of a plate. Additionally, the analysis is used to post-process the resulting plate solution in order to find approximate three-dimensional displacement, strain, and stress distributions throughout the plate. It was decided that the variational-asymptotical method (VAM) would serve as a suitable framework in which to solve these types of problems. Work during this reporting period has progressed along two lines: (1) further evaluation of neo-classical plate theory (NCPT) as applied to shear-coupled laminates; and (2) continued modeling of plates with nonuniform thickness.

Hodges, Dewey H.↗

A critical analysis of the accuracy of several numerical techniques for combustion kinetic rate equations

A detailed analysis of the accuracy of several techniques recently developed for integrating stiff ordinary differential equations is presented. The techniques include two general-purpose codes EPISODE and LSODE developed for an arbitrary system of ordinary differential equations, and three specialized codes CHEMEQ, CREK1D, and GCKP4 developed specifically to solve chemical kinetic rate equations. The accuracy study is made by application of these codes to two practical combustion kinetics problems. Both problems describe adiabatic, homogeneous, gas-phase chemical reactions at constant pressure, and include all three combustion regimes: induction, heat release, and equilibration. To illustrate the error variation in the different combustion regimes the species are divided into three types (reactants, intermediates, and products), and error versus time plots are presented for each species type and the temperature. These plots show that CHEMEQ is the most accurate code during induction and early heat release. During late heat release and equilibration, however, the other codes are more accurate. A single global quantity, a mean integrated root-mean-square error, that measures the average error incurred in solving the complete problem is used to compare the accuracy of the codes. Among the codes examined, LSODE is the most accurate for solving chemical kinetics problems. It is also the most efficient code, in the sense that it requires the least computational work to attain a specified accuracy level. An important finding is that use of the algebraic enthalpy conservation equation to compute the temperature can be more accurate and efficient than integrating the temperature differential equation.

Radhadrishnan, Krishnan↗

CSPlib: A performance portable parallel software toolkit for analyzing complex kinetic mechanisms

Computational singular perturbation (CSP) is a method to analyze dynamical systems. It targets the decoupling of fast and slow dynamics using an alternate linear expansion of the right-hand side of the governing equations based on eigenanalysis of the associated Jacobian matrix. This representation facilitates diagnostic analysis, detection and control of stiffness, and the development of simplified models. For this work, we have implemented CSP in a C++ open-source library CSPlib using the Kokkos parallel programming model to address portability across diverse heterogeneous computing platforms, i.e., multi/many-core CPUs and GPUs. We describe the CSPlib implementation and present its computational performance across different computing platforms using several test problems. Specifically, we test the CSPlib performance for a constant pressure ignition reactor model on different architectures, including IBM Power 9, Intel Xeon Skylake, and NVIDIA V100 GPU. The size of the chemical kinetic mechanism is varied in these tests. As expected, the Jacobian matrix evaluation, the eigensolution of the Jacobian matrix, and matrix inversion are the most expensive computational tasks. When considering the higher throughput characteristic of GPUs, GPUs performs better for small matrices with higher occupancy rate. CPUs gain more advantages from the higher performance of well-tuned and optimized linear algebra libraries such as OpenBLAS.

97 MATHEMATICS AND COMPUTING↗

Unlocking Metamaterials At The Macro Scale (CRADA Final Report)

This project was part of the Cyclotron Road program, which supports scientific entrepreneurs in their efforts to commercialize novel technologies with potential to address energy, manufacturing and climate related issues. The participants' technology is a lightweight cellular material system which could be applied to a range of products and markets and offer benefits of reduced weight, cost, waste, and carbon footprint. The objective of the project was to investigate potential opportunities and de-risk technical and market barriers in pursuit of successful commercialization. This project’s purpose was to find market pathways and technical roadmaps for commercializing the lightweight cellular material technology. The main problems to overcome are the risks in both tech and market. On the technical side, performance, weight, cost and speed of manufacturing, and other scaleup problems needed to be addressed. On the market side, the challenges included finding product/market fit, developing business models and go to market strategies, and developing commercial relationships within various industries. Our approach typically started with market analysis, in order to identify potential applications where our technology could solve problems and address pain points. To do this, we performed customer discovery, interviewing hundreds of industry stakeholders along all parts of the value chain for a given product or industry. From here, we would develop technoeconomic models which combined aspects of numerical modeling for structural and mechanical performance based on criteria from customers or industry guidelines such as stiffness, strength, weight, and other physical properties. Then, this would be combined with detailed cost models to translate the engineering solution into a manufacturable, scalable product. The challenge here was to have equal or better performance at lower cost and higher speed than existing solutions.

36 MATERIALS SCIENCE↗

A programing system for research and applications in structural optimization

The paper describes a computer programming system designed to be used for methodology research as well as applications in structural optimization. The flexibility necessary for such diverse utilizations is achieved by combining, in a modular manner, a state-of-the-art optimization program, a production level structural analysis program, and user supplied and problem dependent interface programs. Standard utility capabilities existing in modern computer operating systems are used to integrate these programs. This approach results in flexibility of the optimization procedure organization and versatility in the formulation of contraints and design variables. Features shown in numerical examples include: (1) variability of structural layout and overall shape geometry, (2) static strength and stiffness constraints, (3) local buckling failure, and (4) vibration constraints. The paper concludes with a review of the further development trends of this programing system.

Sobieszczanski-Sobieski, J.↗

Response of joint dominated space structures

An efficient linearization method is presented for calculating the transient response of nonlinear systems due to initial disturbances. The method is an extension of the describing function approach in which the steady state response of the system is calculated by representing the nonlinear element, typically joints in the case of space structures, by impedances which are functions of the amplitude of response. Thus, the problem of solving the differential equation for the steady state response becomes one of solving a set of nonlinear algebraic equations involving the steady state amplitudes and phases of the system. It is shown that for the transient case the steady state impedances can be averaged over the range of responses in order to provide equivalent values of stiffness and damping that, for a given set of initial displacements, may be treated as being constant for purposes of calculating system response. Single degree of freedom system are used to demonstrate the method and to develop an approach for optimizing the joint's characteristics so as to minimize transient response times. The use of this method for response estimation and optimization in multiple degree of freedom systems is investigated.

Source record↗

Application of artificial neural networks in nonlinear analysis of trusses

A method is developed to incorporate neural network model based upon the Backpropagation algorithm for material response into nonlinear elastic truss analysis using the initial stiffness method. Different network configurations are developed to assess the accuracy of neural network modeling of nonlinear material response. In addition to this, a scheme based upon linear interpolation for material data, is also implemented for comparison purposes. It is found that neural network approach can yield very accurate results if used with care. For the type of problems under consideration, it offers a viable alternative to other material modeling methods.

Alam, J.↗

The Load Distribution in Bolted or Riveted Joints in Light-Alloy Structures

This report contains a theoretical discussion of the load distribution in bolted or riveted joints in light-alloy structures which is applicable not only for loads below the limit of proportionality but also for loads above this limit. The theory is developed for double and single shear joints. The methods given are illustrated by numerical examples and the values assumed for the bolt (or rivet) stiffnesses are based partly on theory and partly on known experimental values. It is shown that the load distribution does not vary greatly with the bolt (or rivet) stiffnesses and that for design purposes it is usually sufficient to know their order of magnitude. The theory may also be directly used for spot-welded structures and, with small modifications, for seam-welded structures, The computational work involved in the methods described is simple and may be completed in a reasonable time for most practical problems. A summary of earlier theoretical and experimental investigations on the subject is included in the report.

Vogt, F.↗

Stress‐constrained topology optimization of structures subjected to nonproportional loading

Abstract This work considers the topology optimization of hyperelastic structures for maximum stiffness (minimum compliance) subject to constraints on their volume and maximum stress. In contrast to almost all previous works, we subject the structures to nonproportional loading, wherein the maximum stress does not necessarily occur at the final load step. As such, the stress is constrained at each load step. The augmented Lagrangian method is used to formulate the optimization problem with its many constraints. In numerical examples, we investigate different load trajectories for the same terminal load and compare the optimized designs and their performances. The results show the importance of considering the entire load trajectory as the load history significantly influences the optimized designs.

42 ENGINEERING↗

Structural model optimization using statistical evaluation

The results of research in applying statistical methods to the problem of structural dynamic system identification are presented. The study is in three parts: a review of previous approaches by other researchers, a development of various linear estimators which might find application, and the design and development of a computer program which uses a Bayesian estimator. The method is tried on two models and is successful where the predicted stiffness matrix is a proper model, e.g., a bending beam is represented by a bending model. Difficulties are encountered when the model concept varies. There is also evidence that nonlinearity must be handled properly to speed the convergence.

Collins, J. D.↗

Improved Benchmarking of Cohesive Elements in Abaqus Standard for Predicting Disbond and Delamination in Composite Structures

Traditional approaches for aircraft certification require the assumption of an initial flaw condition, either represented as barely visible impact damage (BVID) or through inclusion of a Teflon insert to serve as surrogate damage. Based on the initial composite damage state, the structure must be shown to demonstrate structural durability and damage tolerance (DaDT) according to the following criteria: a. Damage displays no detrimental growth under cyclic loading b. The structure is able to sustain design limit load (DLL) Currently, the only available manner for validating structural performance is through test. Since damage can occur over a wide variety of areas within a structure, this approach has proven to be increasingly expensive and time consuming for composite airframes and acreage structure within the design-test-certification building block. A further complicating factor is the requirement to accurately capture the most critical damage morphologies as a starting condition. To understand the severity of the damage, it is either required to experimentally determine the most critical areas at tremendous expense or rely on legacy data of similar structural testing, which limits design space expansion. A preferred solution is to use advanced analysis to provide improved understanding of load margins for critical locations based on a wide variety of potential starting damage conditions. The standard industry approach for DaDT certification adheres to the use of the traditional virtual crack closure technique (VCCT) method. VCCT is generally a preferred method because it conforms to the current certification principles of damage from a known flaw, and when used correctly, can be effective at predicting delamination propagation under static and cyclic loading. The VCCT method requires the inclusion of an initial flaw in the finite element (FE) model requiring a-priori knowledge of the flaw location. This in turn requires a plethora of analysis cases to be examined to cover a reasonable span of potential damage states. Additionally, the VCCT approach requires node-to-node connectivity rendering it incompatible with the best practices and approaches for using continuum damage mechanics (CDM) based progressive damage and failure analysis (PDFA) tools within a typical FE solver. Alternatives to VCCT have emerged in the form of cohesive elements which utilize the cohesive zone model (CZM). Unlike VCCT which models linear elastic fracture mechanics, cohesive elements couples continuum and fracture based responses through the use of bilinear traction separation laws. These laws are defined based on a penalty stiffness, a cohesive strength, and a strain energy release rate. The approach can be mesh regularized with native cohesive elements within many FE solvers such as Abaqus and LS-DYNA. In Phase I of the NASA Advanced Composites Consortium (ACC) post-buckled stiffened panel with BVID, Strength and Life [1], the performance of cohesive elements were benchmarked in comparison to VCCT and LEFM solutions and showed good agreement using Abaqus explicit [2]. To realize savings on current and future programs, it is still necessary to close technical gaps related to the use of cohesive elements with Abaqus Standard. Within a program environment, standard finite element analysis is the preferred analytical capability for quasi-static loading as it eliminates uncertainty due to oscillatory behavior commonly seen with explicit analysis. This oscillatory behavior creates difficulties in writing margins of safety based on the analysis. The use of negative tangent stiffness material models complicates convergence which typically requires the use of numerical controls such as viscous damping to overcome. To date, there has not been a comprehensive study on how to establish best practices for cohesive element convergence for predictive capability within the Abaqus implicit solver. In pursuit of these goals, under the NASA ACC program, several numerical benchmark problems were proposed including pure mode I (double cantilevered beam – DCB), pure mode II (end notch flexure – ENF), and symmetric/unsymmetric evolving mixed mode (single leg bend – SLB). This paper focuses on the use of cohesive elements to model the delamination through the use of CZM. Specifically, finite element models for the DCB, ENF, symmetric SLB, and unsymmetric SLB, are developed and various solution controls for convergence are studied to develop a best practice. Once the best practice has been developed, the predictive capability of the objective CZM model is used to analyze the hat pull-off strength of a standard hat stiffened configuration under various loading conditions.

Abaqus↗

Stability analysis of position and force control problems for robot arms

A stability analysis for robot manipulators under the influence of external forces is presented. Several control objectives are considered: rejecting the external force as a source of disturbance, complying to the external force as a generalized mass-spring-damper system, and actively controlling the external force when a dynamic model for the environment is available. An explanation of instability is given for the case in which the environment has flexibility and the gains are inappropriately chosen. When the environment is stiff in the force control subspace, robust stability can be achieved via the integral force feedback.

Wen, John T.↗

A new uniformly valid asymptotic integration algorithm for elasto-plastic-creep and unified viscoplastic theories including continuum damage

A new scheme to integrate a system of stiff differential equations for both the elasto-plastic creep and the unified viscoplastic theories is presented. The method has high stability, allows large time increments, and is implicit and iterative. It is suitable for use with continuum damage theories. The scheme was incorporated into MARC, a commercial finite element code through a user subroutine called HYPELA. Results from numerical problems under complex loading histories are presented for both small and large scale analysis. To demonstrate the scheme's accuracy and efficiency, comparisons to a self-adaptive forward Euler method are made.

Chulya, A.↗