Showing papers on "Direct stiffness method published in 1994"

A Self-Consistent Fabric Geometry Model: Modification and Application of a Fabric Geometry Model to Predict the Elastic Properties of Textile Composites

Abstract: A method for predicting the elastic properties of textile-reinforced composites is presented with applications. The method is a modification of a Fabric Geometry Model (FGM) [1–3] that relates fiber architecture and material properties of textile-reinforced composites to its global stiffness matrix through micromechanics and stiffness averaging technique. The FGM, although proven to be a quick and successful method [4], suffers two major drawbacks: 1. incompatibility of the basic transverse isotropy assumption with the theoretical mathematical derivation, (i.e., the mathematical derivation produces elastic constants that do not exhibit transverse isotropy) and 2. inconsistency of the transformation matrices associated with the stiffness calculations (i.e., the technique is not sufficiently robust to handle all cases). In this paper, these problems are discussed and solutions are presented. Comparison between stiffness and compliance averaging approaches is investigated. Moreover, predictions using the Self-Consistent FGM are compared with experimental data available in literature.

An active flexible wing multi-disciplinary design optimization method

Abstract: This paper discusses Active Flexible Wing (AFW) technology and describes how it differs from conventional wing design. The benefits of AFW are briefly described. Two design procedures which aid in the design and optimization of an AFW wing are described in detail. The first procedure is for the design of an AFW control system on an existing wing. This procedure optimizes control surface positions to maximize air vehicle maneuverability, without exceeding structural limits. The second procedure is for the design of a new wing using AFW technology. This procedure simultaneously couples aerodynamic, structural, and external load designs. The process optimizes a wing structure and control surface positions for minimum weight and drag, while satisfying structural constraints. = buckling constraints = bending moment = drag of case i = hinge moment = roll moment of load case i = lift of load case i = pitching moment of load case i = roll rate = torsion moment = twist and camber variables (e.g., wing jig shape design) = structural design variables = flutter constraints = structural weight = control surface positions and air vehicle flight angle design variables = roll axis inertia = roll acceleration = stress constraints of load case i {a} = vector of rigid aerodynamic panel deflections {!} = lift vector on aerodynamic panels * Project Engineer, Advanced Aircraft Member AIAA [ A ] = aerodynamic panel lift due to alpha influence coefficient matrix [ B ] = aerodynamic to structural transformation matrix [ K ] = global stiffness matrix [ d ~ / dtk] = derivative of the global structural stiffness matrix with respect to structural design variables [ S I ] =structural flexibility matrix (in units of deflection per force) on aerodynamic model [ S A ] = structural flexibility matrix (in units of rotation per force) on aerodynamic model

Computer aided design system

Abstract: In a computer aided design system, a stored geometrical representation of a structure, the material properties thereof, and the loads imposed thereon are converted into a visualization of a mechanical quantity of the structure. A mesh is generated that describes the structure. By application of the finite element method to the mesh, the elements of a stiffness matrix, a loading vector and a vector including an associated degree of freedom index for each row and column of the stiffness matrix is generated. From the stiffness matrix and the loading vector, a matrix A and a right-hand side vector f are generated. A and f are related through the equation Ax=f, wherein the vector x represents the mechanical quantity at points of the mesh. A linear solver of the preconditioned conjugate gradient-type generates the elements of the vector x from A and f using a preconditioning matrix K. The linear solver generates a principal submatrix from the stiffness matrix by setting to zero those elements therein and positioned such that the degree of freedom index associated with their row is not equal to the degree of freedom index associated with their column. The linear solver also generates the preconditioning matrix K from the principal submatrix. The mechanical quantity of the structure is visualized on the computer aided design system as a function of the vector x.

Stiffness matrix of the four‐node quadrilateral element in closed form

Abstract: The stiffness matrix of a plane four-node quadrilateral finite element is given in closed form. When expressed as a FORTRAN subroutine and compared with the classical method of forming the stiffness matrix using Gaussian integration, the approach gives a CPU time speed-up of the order of 2–3 on a vector machine and of the order of 4–5 on a scalar machine. The technique used to generate the terms of the stiffness matrix made use of a computer algebra system which could clearly be extended to generate the matrices for other elements types.

The analysis of cable and catenary structures

Abstract: * Analysis of general two-dimensional cable structures * The contribution of individual element stiffness to the overall structural stiffness matrix * The method of solution of the non-linear stiffness equations * Computer program flow chart * Analysis of three * Dimensional cable structures * Appendices

An Exact Stiffness Method for Elastodynamics of a Layered Orthotropic Half-Plane

Abstract: The half plane region under consideration consists of a number of layers with different thicknesses and material properties. Exact layer stiffness matrices describing the relationship between Fourier transforms of displacements and tractions at the upper and bottom surface of each layer are established explicitly by using the analytical general solutions for displacements and stresses of a homogeneous orthotropic elastic medium.The global stiffness matrix which is also symmetric and banded is assembled by considering the traction continuity conditions at the interface between adjacent layers of the multilayered half plane

Stiffness analysis and control of redundant manipulators

Abstract: In this paper, two points are addressed as for the stiffness control of redundant manipulators. The first is, through the joint stiffness analysis, a generalized stiffness model between the joint and taskspace stiffness. Differing from the previous stiffness model, this model shows the existence of the additional stiffness concerning the configuration change and force. The second is the joint stiffness control scheme of redundant manipulators based on the developed model, called orthogonal stiffness decomposition control. The effectiveness of the proposed model and control method is verified through simulations and experiments. >

Equivalent Continuum Model for Deployable Flat Lattice Structures

Abstract: Deployable structures can be stored in a compact, folded configuration and are easily deployed into load-bearing, open forms. Hence, they are suitable for applications where speed and ease of erection and reusability are desired. The structures investigated here are prefabricated space frames made of so called scissor-like elements, sets of two straight bars connected to each other by a pivot. These structures are stress-free and self-standing in both their folded and deployed configurations, thus overcoming major disadvantages of previous designs. This study deals with deployable structures that are flat and subjected to normal loads in their deployed configuration. Although the behavior for that loading case is linear, the availability of an equivalent continuum model for stiffness prediction is desirable because it can significantly reduce the computational effort during preliminary design. The derivation of such a model is not straightforward because of the unorthodox geometry and the rotations allowed by the hinged and pivotal connections. This problem is addressed by first applying the direct stiffness method within a symbolic manipulation framework to transform the lattice structure to an equivalent single-layer grid, and then using existing expressions to obtain the desired equivalent plate. The model exhibits good accuracy and convergence characteristics for uniform loads.

Object-oriented optimization of discrete structures

Abstract: A new object-oriented method is proposed for the optimum design of discrete structures being subjected to various local and global constraints. The method uses an element-based information and procedures instead of the global ones such as a global stiffness matrix and calculating of the inverse of a matrix. The principle of the method is that each element is able to evaluate its resource margins with respect to vaious local and global constraints, and the element reduce its resource based on the minimum of those resource margins. This simple procedure is used iteratively to obtain an optimum solution. It is found from several numerical experiments that the proposed method is effective for the optimum design of discrete structures such as trusses.

Exact and Direct Modeling Technique for Rotor-Bearing Systems with Arbitrary Selected Degrees-of-Freedom

Abstract: An exact and direct modeling technique is proposed for modeling of rotor-bearing systems with arbitrary selected degrees-of-freedom. This technique is based on the combination of the transfer and dynamic stiffness matrices. The technique differs from the usual combination methods in that the global dynamic stiffness matrix for the system or the subsystem is obtained directly by rearranging the corresponding global transfer matrix. Therefore, the dimension of the global dynamic stiffness matrix is independent of the number of the elements or the substructures. In order to show the simplicity and efficiency of the method, two numerical examples are given.

A bar finite element for vibration and buckling analysis of cracked truss constructions

Abstract: The paper presents a method of forming an inertia matrix and linear and geometrical stiffness matrices of a bar finite element with a single, non-propagating transverse one-edge open crack located in its mid-length. The presented method is based on the displacement formulation of FEM and laws of fracture mechanics. It has been found that the crack modified the inertia matrix and the linear stiffness matrix of the element, whereas the geometrical stiffness matrix remained unchanged. Taking advantage of the presented element there were done exemplary numerical calculations illustrating variations of longitudinal natural frequencies of the one sided fixed rod and variations of the values of global buckling load in a simple truss caused by the crack. The effect of inertia matrix form upon the values of longitudinal natural frequencies of the one sided fixed rod were analyzed.

Essential features in the chemistry of burning systems dissociation reactions

Abstract: A direct stiffness method of analyzing the elastic ftexural-torsional buckling of rigid-jointed plane frames composed of l-section members and subjected to in-plane loads is presented. The in-plane stiffness matrix and the fixed-end resultants are obtained from the member stiffness matrices derived from the in-plane differential equations. These member stiffness matrices are assembled and solved, and their solutions are used to linearize the flexural-torsional buckling equations. The out-of-plane member stiffness matrices are then obtained numerically from the buckling equations by the method of finite integrals. The out-of-plane frame -stiffness matrix is assembled, and the critical loads are obtained when its determinant is zero. A computer program is developed which carries out either a first- or second-order in-plane analysis, and then determines the flexural-torsional buckling loads. The effects of in-plane deformations prior to buckling can be included. Very good agreement is obtained betwe...