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At least 145 records · Page 8

Adaptive remeshing method for finite-element thermal analysis

A finite-element remeshing approach that makes use of quadrilateral and triangular elements is described. The approach uses the solution on a previous mesh to create a new mesh. Meshes are completely unstructured with highly refined elements in regions of steep gradients and larger elements where gradients are smaller. Studies of convergence rates for heat conduction problems with exact solutions show that for problems with highly localized solution variations, the remeshing approach gives smaller solution errors with fewer unknowns than refinement of uniform, structured meshes.

Thornton, Earl A.↗

Accuracy of Gradient Reconstruction on Grids with High Aspect Ratio

Gradient approximation methods commonly used in unstructured-grid finite-volume schemes intended for solutions of high Reynolds number flow equations are studied comprehensively. The accuracy of gradients within cells and within faces is evaluated systematically for both node-centered and cell-centered formulations. Computational and analytical evaluations are made on a series of high-aspect-ratio grids with different primal elements, including quadrilateral, triangular, and mixed element grids, with and without random perturbations to the mesh. Both rectangular and cylindrical geometries are considered; the latter serves to study the effects of geometric curvature. The study shows that the accuracy of gradient reconstruction on high-aspect-ratio grids is determined by a combination of the grid and the solution. The contributors to the error are identified and approaches to reduce errors are given, including the addition of higher-order terms in the direction of larger mesh spacing. A parameter GAMMA characterizing accuracy on curved high-aspect-ratio grids is discussed and an approximate-mapped-least-square method using a commonly-available distance function is presented; the method provides accurate gradient reconstruction on general grids. The study is intended to be a reference guide accompanying the construction of accurate and efficient methods for high Reynolds number applications

Thomas, James↗

NASTRAN finite element idealization study

The investigation of the effects of variations of mesh refinement and mesh pattern were conducted using a basic rectangular mesh pattern. When employing the constant strain TRMEM element, the basic rectangular pattern was subdivided into triangles. This subdivision employs two different triangular patterns and allows results to be obtained which demonstrate the effect of modelling bias. Errors in tip deflection, direct stress, and shearing stress as a function of mesh size and element aspect ratio were obtained as well as mid-span stress distributions. All problems were solved on an IBM 360/95 computer using MacNeal-Schwendler Version MSC-38 Rigid Format-1 of the NASTRAN computer program. While NASTRAN uses double precision arithmetic for the solution of the global equations for displacements, subsequent computations to obtain element stresses are carried out in single precision. This suggests that some improvement in stress recovery might be expected when using the higher precision DCD machines.

Case, W. R.↗

Self-Avoiding Walks Over Adaptive Triangular Grids

Space-filling curves is a popular approach based on a geometric embedding for linearizing computational meshes. We present a new O(n log n) combinatorial algorithm for constructing a self avoiding walk through a two dimensional mesh containing n triangles. We show that for hierarchical adaptive meshes, the algorithm can be locally adapted and easily parallelized by taking advantage of the regularity of the refinement rules. The proposed approach should be very useful in the runtime partitioning and load balancing of adaptive unstructured grids.

Heber, Gerd↗

New plate and shell elements for NASTRAN

A new higher order triangular plate-bending finite element is presented which possesses high accuracy for practical mesh subdivisions and which uses only translations and rotations as grid point degrees of freedom. The element has 18 degrees of freedom, the transverse displacement and two rotations at the vertices and mid-side grid points of the triangle. The transverse displacement within the element is approximated by a quintic polynomial; the bending strains thus vary cubically within the element. Transverse shear flexibility is taken into account in the stiffness formulation. Two examples of static and dynamic analysis are included to show the behavior of the element.

Narayanaswami, R.↗

A Solar Sail Shape Modeling Approach for Attitude Control Design and Analysis

Solar sails operating in the space environment experience deformations in sail shape that result in relatively large disturbance torques which dictate the required performance of the spacecraft attitude control and momentum management systems. These deformations are driven by thermal loads on the booms (due to uneven solar heating), manufacturing and assembly tolerances, and variations in membrane tension. The Solar Cruiser spacecraft utilizes a four-quadrant sail design with four 30-meter length booms and four triangular sail membranes, creating a square sail structure of >1600 m2. Medium-fidelity mesh models were developed based on a characteristic deformed shape. A series of parametric studies were conducted using this shape paradigm to determine worst-case deformed sail shapes which produce bounding disturbance torques. A large database of shapes was produced, and the forces and moments induced by each individual shape were calculated using a Rios-Reyes reduced order generalized sail model. Two were selected as reference worst-case shapes for the Solar Cruiser mission: one which produced the highest pitch/yaw root-sum-squared (RSS) torque, and one which produced the highest roll torque. The results showed that the worst-case shapes at high solar incidence angles induce significantly higher (2-10x) disturbance torques than an ideal, flat-plate sail. Even with considerable safety margins, assuming an ideal sail is unlikely to sufficiently bound the disturbances, which is critical when designing the attitude control system and sizing actuators. Accurate sail shape modeling methodologies should therefore be employed on future solar sail missions.

Solar Sail↗

A Solar Sail Shape Modeling Approach for Attitude Control Design and Analysis

Solar sails operating in the space environment experience deformations in sail shape that result in relatively large disturbance torques which dictate the required performance of the spacecraft attitude control and momentum management systems. These deformations are driven by thermal loads on the booms (due to uneven solar heating), manufacturing and assembly tolerances, and variations in membrane tension. The Solar Cruiser spacecraft utilizes a four-quadrant sail design with four 30-meter length booms and four triangular sail membranes, creating a square sail structure of >1600 m2. Medium-fidelity mesh models were developed based on a characteristic deformed shape. A series of parametric studies were conducted using this shape paradigm to determine worst-case deformed sail shapes which produce bounding disturbance torques. A large database of shapes was produced, and the forces and moments induced by each individual shape were calculated using a Rios-Reyes reduced order generalized sail model [1]. Two were selected as reference worst-case shapes for the Solar Cruiser mission: one which produced the highest pitch/yaw root-sum-squared (RSS) torque, and one which produced the highest roll torque. The results showed that the worst-case shapes at high solar incidence angles induce significantly higher (2-10x) disturbance torques than an ideal, flat-plate sail. Even with considerable safety margins, assuming an ideal sail is unlikely to sufficiently bound the disturbances, which is critical when designing the attitude control system and sizing actuators. Accurate sail shape modeling methodologies should therefore be employed on future solar sail missions. References [1] L. Rios-Reyes and D. J. Scheeres, “Generalized Model for Solar Sails,” Journal of Spacecraft and Rockets, Vol. 42, Jan. 2005, pp. 182–185, 10.2514/1.9054.

Solar Sail↗

A Novel Four-Node Quadrilateral Smoothing Element for Stress Enhancement and Error Estimation

A four-node, quadrilateral smoothing element is developed based upon a penalized-discrete-least-squares variational formulation. The smoothing methodology recovers C1-continuous stresses, thus enabling effective a posteriori error estimation and automatic adaptive mesh refinement. The element formulation is originated with a five-node macro-element configuration consisting of four triangular anisoparametric smoothing elements in a cross-diagonal pattern. This element pattern enables a convenient closed-form solution for the degrees of freedom of the interior node, resulting from enforcing explicitly a set of natural edge-wise penalty constraints. The degree-of-freedom reduction scheme leads to a very efficient formulation of a four-node quadrilateral smoothing element without any compromise in robustness and accuracy of the smoothing analysis. The application examples include stress recovery and error estimation in adaptive mesh refinement solutions for an elasticity problem and an aerospace structural component.

Tessler, A.↗

A structured and unstructured remeshing method for high speed flows

An adaptive remeshing method using both triangular and quadrilateral elements suitable for high speed flows is presented. For inviscid flows the method generates completely unstructured meshes. For viscous flows the boundary layer edge is identified adaptively and a structured mesh is generated in the boundary layer, and an unstructured mesh is generated in the inviscid region. Examples of inviscid and viscous mesh adaptations for high speed flows are presented. A comparison is made between first order and higher order finite element algorithms when used in association with the remeshing method.

Vemaganti, Gururaja R.↗

Finite element analysis of high speed compressible flows using mesh refinement/movement procedures

An adaptive mesh refinement procedure for analyzing high-speed inviscid and viscous compressible flows is described. The adaptation procedure which uses both quadrilateral and triangular elements is implemented with an explicit finite element formulation. Elements in regions of strong and weak gradients are refined or coarsened based on inviscid and viscous indicators. Nodal locations are also adaptively moved to better resolve flow features. The effectiveness of the finite element procedure is demonstrated by modeling flows with complex shock structure and viscous-inviscid interactions. Numerical results are compared with experimental data.

Ramakrishnan, R.↗

Adaptive finite element analysis of hypersonic laminar flows for aerothermal load predictions

The use of an adaptive mesh refinement procedure for analyzing hypersonic laminar flows with application to aerothermal load predictions is described. The adaptation procedure, which uses both quadrilateral and triangular elements, is implemented with the multistep Galerkin-Runge-Kutta scheme. Elements that lie in regions of strong gradients are refined based on indicators to obtain better definition of flow features. The effectiveness of the adaptive procedure is demonstrated by modeling Mach 11.7 flow over a 15-deg ramp. Numerical results are compared with predictions of strong interaction theories and experimental data. Surface quantities such as heating rates and pressure loads, critical for the effective design of high-speed vehicles, are found to be in good agreement with experimental values.

Ramakrishnan, R.↗

Unstructured 3D Delaunay mesh generation applied to planes, trains and automobiles

Technical issues associated with domain-tessellation production, including initial boundary node triangulation and volume mesh refinement, are presented for the 'TGrid' 3D Delaunay unstructured grid generation program. The approach employed is noted to be capable of preserving predefined triangular surface facets in the final tessellation. The capabilities of the approach are demonstrated by generating grids about an entire fighter aircraft configuration, a train, and a wind tunnel model of an automobile.

Blake, Kenneth R.↗

ELAS: A general-purpose computer program for the equilibrium problems of linear structures. Volume 2: Documentation of the program

A general purpose digital computer program for the in-core solution of linear equilibrium problems of structural mechanics is documented. The program requires minimum input for the description of the problem. The solution is obtained by means of the displacement method and the finite element technique. Almost any geometry and structure may be handled because of the availability of linear, triangular, quadrilateral, tetrahedral, hexahedral, conical, triangular torus, and quadrilateral torus elements. The assumption of piecewise linear deflection distribution insures monotonic convergence of the deflections from the stiffer side with decreasing mesh size. The stresses are provided by the best-fit strain tensors in the least squares at the mesh points where the deflections are given. The selection of local coordinate systems whenever necessary is automatic. The core memory is used by means of dynamic memory allocation, an optional mesh-point relabelling scheme and imposition of the boundary conditions during the assembly time.

Utku, S.↗

Directionally adaptive finite element method for multidimensional Euler and Navier-Stokes equations

A directionally adaptive finite element method for multidimensional compressible flows is presented. Quadrilateral and hexahedral elements are used because they have several advantages over triangular and tetrahedral elements. Unlike traditional methods that use quadrilateral/hexahedral elements, our method allows an element to be divided in each of the three directions in 3D and two directions in 2D. Some restrictions on mesh structure are found to be necessary, especially in 3D. The refining and coarsening procedures, and the treatment of constraints are given. A new implementation of upwind schemes in the constrained finite element system is presented. Some example problems, including a Mach 10 shock interaction with the walls of a 2D channel, a 2D viscous compression corner flow, and inviscid and viscous 3D flows in square channels, are also shown.

Tan, Zhiqiang↗

A finite dynamic element for laminated composite plates and shells

Development of finite dynamic elements can result in a significant reduction of computing time and cost for calculation of natural frequencies and mode shapes, which is an essential part of flutter prediction. Analysis with and without the dynamic terms is an alternative to constructing a new finite element mesh, to determine whether the mesh is sufficiently refined. Finite dynamic elements show spectacular improvement in convergence of higher modes with mesh refinement, but the improvement for lower modes is not so great. Cost reduction ratios greater than 20 have been observed for some modes. An average cost reduction ratio of 12 was achieved for the first six modes of a swept, tapered sandwich composite plate, at the 3 percent error level. Another set of calculations was made to determine the mesh density and cost parameters for which none of the first 12 frequencies was in error by more than 3 percent. It was found that the computing cost parameter for the dynamic element was about three times lower than the basic triangular element and 5.9 times lower than an eight-node isoparametric element.

Martin, C. W.↗

Finite element Euler computations in three dimensions

A two-step explicit FEM solution algorithm for the three-dimensional compressible Euler and Navier-Stokes equations based on unstructured triangular and tetrahedral grids is described and demonstrated. The method represents an extension and refinement of the algorithms presented by Loehner et al. (1984 and 1985), Peraire et al. (1987), and Morgan et al. (1987). The formulation and numerical implementation are outlined; the mesh generation, data structures, and adaptive remeshing are explained; and results for a two-dimensional airfoil, a three-dimensional engine air intake, a B747 in landing configuration, and a generic fighter aircraft are presented in extensive graphics and discussed in detail.

Peraire, Jaime↗

An adaptive finite element method for high speed flows

The solution of the equations of compressible high speed flow, on unstructured triangular grids in 2D and tetrahedral grids in 3D, is considered. Solution methods based upon both Taylor-Galerkin and Runge-Kutta time-stepping techniques are presented and the incorporation of the ideas of flux corrected transport (FCT) is discussed. These methods are combined with an adaptive mesh regeneration procedure and are employed in the solution of several examples, consisting of Euler flows in both 2D and 3D and Navier-Stokes flows in 2D.

Peraire, J.↗

Triangular Element For Analyzing Elasticity Of Laminates

Flat triangular element developed for use in finite-element analyses of stress and strain in laminated plates made of such materials as plywood or advanced fiber/epoxy composite materials. Has multiple layers, each of which can have different isotropic or orthotropic elastic properties. Many such elements used in finite-element mesh to calculate stiffness of plate. Formulation of element straight-forward, and calculation of its stiffness matrix simple and fast.

Martin, C. Wayne↗