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Program starts at micromechanical level, from simple inputs supplied by user. COMGEN, COmposite Model GENerator, is interactive FORTRAN program used to create wide variety of finite-element models of continuous-fiber composite materials at micromechanical level. Quickly generates batch or "session files" to be submitted to finite-element preprocessor and postprocessor program, PATRAN. COMGEN requires PATRAN to complete model.
The implementation of a computer code CONE (for C(1) continuity) based on the p-version of the finite element method is described. A hierarchic family of triangular finite elements of degree p 5 is used. This family enforces C(1)-continuity across interelement boundaries, and the code is applicable to fourth order partial differential equations in two independent variables, in particular to the biharmonic equation. Applications to several benchmark problems in plate bending are presented. Sample results are examined and compared with theoretical predictions. In particular the analysis of the bending of a rhombic plate shows a significant improvement over othr published results.
The present study is concerned with the development of a mixed shear flexible finite element with relaxed continuity for the geometrically linear and nonlinear analysis of laminated anisotropic plates. The formulation of the element is based on a refined higher-order theory. This theory satisfies the zero transverse shear stress boundary conditions on the top and bottom faces of the plate. Shear correction coefficients are not needed. The developed element consists of 11 degrees-of-freedom per node, taking into account three displacements, two rotations, and six moment resultants. An evaluation of the element is conducted with respect to the accuracy obtained in the bending of laminated anistropic rectangular plates with different lamination schemes, loadings, and boundary conditions.
The use of eddy current techniques for characterizing flaws in graphite-based filament-wound cylindrical structures is described. A major emphasis was also placed upon incorporating artificial intelligence techniques into the signal analysis portion of the inspection process. Developing an eddy current scanning system using a commercial robot for inspecting graphite structures (and others) was a goal in the overall concept and is essential for the final implementation for the expert systems interpretation. Manual scans, as performed in the preliminary work here, do not provide sufficiently reproducible eddy current signatures to be easily built into a real time expert system. The expert systems approach to eddy current signal analysis requires that a suitable knowledge base exist in which correct decisions as to the nature of a flaw can be performed. A robotic workcell using eddy current transducers for the inspection of carbon filament materials with improved sensitivity was developed. Improved coupling efficiencies achieved with the E-probes and horseshoe probes are exceptional for graphite fibers. The eddy current supervisory system and expert system was partially developed on a MacIvory system. Continued utilization of finite element models for predetermining eddy current signals was shown to be useful in this work, both for understanding how electromagnetic fields interact with graphite fibers, and also for use in determining how to develop the knowledge base. Sufficient data was taken to indicate that the E-probe and the horseshoe probe can be useful eddy current transducers for inspecting graphite fiber components. The lacking component at this time is a large enough probe to have sensitivity in both the far and near field of a thick graphite epoxy component.
An overview of the capabilities of the CHarring Ablator Response (CHAR) code is presented. CHAR is a one-, two-, and three-dimensional unstructured continuous Galerkin finite-element heat conduction and ablation solver with both direct and inverse modes. Additionally, CHAR includes a coupled linear thermoelastic solver for determination of internal stresses induced from the temperature field and surface loading. Background on the development process, governing equations, material models, discretization techniques, and numerical methods is provided. Special focus is put on the available boundary conditions including thermochemical ablation, surface-to-surface radiation exchange, and flowfield coupling. Finally, a discussion of ongoing development efforts is presented.
An overview of the capabilities of the CHarring Ablator Response (CHAR) code is presented. CHAR is a one-, two-, and three-dimensional unstructured continuous Galerkin finite-element heat conduction and ablation solver with both direct and inverse modes. Additionally, CHAR includes a coupled linear thermoelastic solver for determination of internal stresses induced from the temperature field and surface loading. Background on the development process, governing equations, material models, discretization techniques, and numerical methods is provided. Special focus is put on the available boundary conditions including thermochemical ablation and contact interfaces, and example simulations are included. Finally, a discussion of ongoing development efforts is presented.
A general method of error analysis and correction is investigated for the discrete finite-element results for cylindrical shell structures. The method for error analysis is an adaptation of the method of successive approximation. When applied to the equilibrium equations of shell theory, successive approximations derive an approximate continuous solution from the discrete finite-element results. The advantage of this continuous solution is that it contains continuous partial derivatives of an order higher than the basis functions of the finite-element solution. Preliminary numerical results are presented in this paper for the error analysis of finite-element results for a postbuckled stiffened cylindrical panel modeled by a general purpose shell code. Numerical results from the method have previously been reported for postbuckled stiffened plates. A procedure for correcting the continuous approximate solution by Newton's method is outlined.
The accurate calculation of stresses at boundaries and interfaces where FEM analysis may be unreliable is presently undertaken by an error analysis that derives a continuous approximation to discrete finite-element data, which can be differentiated to compute continuous stresses for component-failure predictions. An evaluation is conducted of this approximation in the context of the nonlinear PDEs. A novel interpolation formula which is a simple modification of the double Fourier sine series is used to reduce truncation errors near the rectangular plate boundary by means of an 'extended grid'. Results are presented from a FEM solution, a conventional double-Fourier series' continuous approximation, and a solution applying interpolation on the extended grid, which yields superior convergence properties near the plate boundaries.
The paper deals with a method of optimizing harmonically or dynamically excited structures which removes the frequency constraint (that specifies that the structure's first natural frequency of vibration must be greater than the excitation frequency), replaces the displacement constraint by an inequality constraint on the allowable stress and applies finite element approximations to the continuous one-dimensional structures. When the problem is posed in this manner, the feasible design space is disconnected or 'disjoint'. An attempt is made to explain this disjointness by studying the optimal design of a thin-walled cantilevered rod subjected to steady, simple harmonic torsional excitation. The finite element method is applied to the optimization of a harmonically excited structure with an arbitrary number of design variables, with the disjointness of the design space, a complicating factor.
It is well-known that stresses (and strains) calculated by a displacement-based finite element analysis are generally not as accurate as the displacements. In addition, the calculated stress field is typically discontinuous at element interfaces. Because the stresses are typically of more interest than the displacements, several procedures have been proposed to obtain a smooth stress field, given the finite element stresses, and to improve the accuracy. Hinton and Irons introduced global least squares smoothing of discrete data defined on a plane using a finite element formulation. Tessler and co-workers recently developed a conceptually similar formulation for smoothing of two-dimensional data based on a discrete least square approximation with a penalty constraint. The penalty constraint results in a stress field which is C(exp 1)-continuous, a result not previously obtained. The approach requires additional, 'smoothing' finite element analysis and for their two-dimensional application, they used a conforming C(exp 0)-continuous triangular finite element based on a conforming plate element. This paper presents the results of a detailed investigation into the application of Tessler's smoothing procedure to the smoothing of finite element stresses from one-dimensional problems. Although the one-dimensional formulation has some practical applicability, such as in truss, beam, axisymmetric mechanics, and one-dimensional heat conduction, the primary motivation for developing the one-dimensional smoothing case is to explore the characteristics of the general smoothing strategy. In particular, it is used to describe the behavior of the method and to explore the suitability of criteria proposed for the smoothing analysis. Prior to presenting numerical results, the variational formulation of the smoothing strategy is presented and a criterion for the smoothing analysis is described.
The various phases to developing a methodology for studying the response of a spring-reinforced arch subjected to a point load are discussed. The arch is simply supported at its ends with both the spring and the point load assumed to be at midspan. The spring is present to off-set the typical snap through behavior normally associated with arches, and to provide a structure that responds with constant resistance over a finite displacement. The various phases discussed consist of the following: (1) development of the closed-form solution for the shallow arch case; (2) development of a finite difference analysis to study (shallow) arches; and (3) development of a finite element analysis for studying more general shallow and nonshallow arches. The two numerical analyses rely on a continuation scheme to move the solution past limit points, and to move onto bifurcated paths, both characteristics being common to the arch problem. An eigenvalue method is used for a continuation scheme. The finite difference analysis is based on a mixed formulation (force and displacement variables) of the governing equations. The governing equations for the mixed formulation are in first order form, making the finite difference implementation convenient. However, the mixed formulation is not well-suited for the eigenvalue continuation scheme. This provided the motivation for the displacement based finite element analysis. Both the finite difference and the finite element analyses are compared with the closed form shallow arch solution. Agreement is excellent, except for the potential problems with the finite difference analysis and the continuation scheme. Agreement between the finite element analysis and another investigator's numerical analysis for deep arches is also good.
A benchmark example based on the Calibrated End-Loaded Split (C-ELS) specimen is developed and used to assess the performance of recently developed delamination propagation capabilities in the Abaqus/Standard finite element code. The C-ELS specimen has the advantage of a longer region of stable delamination propagation compared to the existing mode II benchmark case. The new benchmark example may therefore provide a better assessment tool by enabling more stable crack growth in regions further away from the boundary conditions or load application. First, a benchmark result is created manually using two-dimensional finite element models of the C-ELS specimen with different delamination lengths. Second, the performance of the delamination propagation capabilities in the Abaqus/Standard finite element code are assessed by comparing the results to the benchmark case. Two examples with different starter delamination lengths are studied. A shorter starter length is chosen to create a scenario with unstable delamination propagation. A longer delamination causes stable delamination propagation. Detailed results from three-dimensional analyses with aligned and mis-aligned meshes and two levels of mesh refinement are provided for several permutations of numerical input parameters. In general, good agreement can be achieved between the results obtained from the quasi-static propagation analysis and the benchmark analysis. However, particular non-default settings are found to be most reliable, accurate, and numerically efficient. Numerical artifacts including anomalous unreleased nodes in the crack wake and zig-zag crack fronts occur, and further development of the Abaqus/Standard VCCT propagation may be required. Use of the benchmark case to assess the continuous improvements in one finite element code illustrates the value of establishing benchmark solutions.
Continuous media nonlinear thermomechanical behavior, presenting finite element formulation of deformation and irreversible thermodynamics problems
During the past 6 months, efforts were concentrated on the following areas: (1) Continued development of realistic, finite element modeling of plate interactions and associated deformation in the Eastern Mediterranean; (2) Neotectonic field investigations of seismic faulting along the active fault systems in Turkey with emphasis on identifying seismic gaps along the North Anatolian fault; and (3) Establishment of a GPS regional monitoring network in the zone of ongoing continental collision in eastern Turkey (supported in part by NSF).
This report describes theoretical background material and commands necessary to use the WARP3D finite element code. WARP3D is under continuing development as a research code for the solution of very large-scale, 3-D solid models subjected to static and dynamic loads. Specific features in the code oriented toward the investigation of ductile fracture in metals include a robust finite strain formulation, a general J-integral computation facility (with inertia, face loading), an element extinction facility to model crack growth, nonlinear material models including viscoplastic effects, and the Gurson-Tver-gaard dilatant plasticity model for void growth. The nonlinear, dynamic equilibrium equations are solved using an incremental-iterative, implicit formulation with full Newton iterations to eliminate residual nodal forces. The history integration of the nonlinear equations of motion is accomplished with Newmarks Beta method. A central feature of WARP3D involves the use of a linear-preconditioned conjugate gradient (LPCG) solver implemented in an element-by-element format to replace a conventional direct linear equation solver. This software architecture dramatically reduces both the memory requirements and CPU time for very large, nonlinear solid models since formation of the assembled (dynamic) stiffness matrix is avoided. Analyses thus exhibit the numerical stability for large time (load) steps provided by the implicit formulation coupled with the low memory requirements characteristic of an explicit code. In addition to the much lower memory requirements of the LPCG solver, the CPU time required for solution of the linear equations during each Newton iteration is generally one-half or less of the CPU time required for a traditional direct solver. All other computational aspects of the code (element stiffnesses, element strains, stress updating, element internal forces) are implemented in the element-by- element, blocked architecture. This greatly improves vectorization of the code on uni-processor hardware and enables straightforward parallel-vector processing of element blocks on multi-processor hardware.
A new iterative solution technique for predicting the sound field radiated from a turbofan inlet in steady flight is presented. The sound field is divided into two regions: the sound field within and near the inlet which is computed using the finite element method and the radiation field beyond the inlet which is calculated using an integral solution technique. A continuous solution is obtained by matching the finite element and integral solutions at the interface between the two regions. The applicability of the iterative technique is demonstrated by comparison of experimental results with the theoretical results for several different inlet configurations with and without flow. These examples show that good agreement between experiment and theory is obtained within five iterations.
An iterative solution technique for predicting the sound field radiated from a turbofan inlet is used to predict the optimum inlet acoustic liner. The analytical approach divides the sound field into two regions: the sound field within and near the inlet which is computed using the finite element method and the radiation field beyond the inlet which is calculated using an integral solution technique. A continuous solution is obtained by matching the finite element and integral solutions at the interface between the two regions. Using a trial and error scheme, this analytical procedure is used to calculate the impedance value of the duct liner which will produce a minimum sound pressure level in the far field. Several examples of straight and non-uniform ducts with and without flow are presented.
A variable fidelity, multiscale, physics based finite element procedure for predicting progressive damage and failure of laminated continuous fiber reinforced composites is introduced. At every integration point in a finite element model, progressive damage is accounted for at the lamina-level using thermodynamically based Schapery Theory. Separate failure criteria are applied at either the global-scale or the microscale in two different FEM models. A micromechanics model, the Generalized Method of Cells, is used to evaluate failure criteria at the micro-level. The stress-strain behavior and observed failure mechanisms are compared with experimental results for both models.