Showing papers on "Direct stiffness method published in 1979"

Matrix Structural Analysis

Abstract: Examines computerized structural analysis methods for buildings, bridges, and other structures, with special emphasis on current practices. Covers the stiffness analysis of frames, the flexibility method, virtual work principles, special analysis procedures, and more. Defines the terminology, coordinate systems, and fundamental concepts of structural behavior, laying the foundation for the study of more advanced treatments such as the finite element method.

Derivation of a new stiffness matrix for helically armoured cables considering tension and torsion

Abstract: A new element stiffness matrix is derived for straight cable elements subjected to tension and torsion The cross-section of a cable, which may consist of many different structural components, is treated in the following as a single composite element The derivation is quite general; consequently, the results can be used for a broad category of cable configurations Individual helical armourning wires, for instance, may have unique geometric and material properties In addition, no limit is placed on the number of wire layers Furthermore, compressibility of the central core element can also be considered The equations of equilibrium are first derived to include ‘internal’ geometric non-linearties produced by large deformations (axial elongation and rotatioin) of a straight cable element These equations are then linearized in a consistent manner to give a liner stiffness matrix Linear elasticity is assumed throughout Excellent agreement with experimental results for two different cables validates the correctness of the analysis

Shear Correction Factors for Laminated Plates

Abstract: S HEAR deformations are considered in laminated plate theory in terms of correction factors ktj (or k-j) and modified shear stiffnesses K^ — k^A^ = k-jA^; (ij = 4,5), where AJJ (or A-J) are obtained from assumed "constant strain (or stress)" fields.1 This work reports the correction factors, obtained by matching cutoff frequencies for propagation of thickness shear waves (ratio of wavelength X to plate thickness H approaching infinity) predicted by plate and elasticity theories. Contents For an exact elasticity solution, the stiffness matrix relating tractions to displacements on the surfaces of each layer is expressed as a function of shear moduli and frequency.2 Cutoff frequencies co/2 for the first two modes dominated by strains yxz and yyz, respectively, are calculated such that determinant of the global stiffness matrix goes to zero. k'n are then evaluated as Kn/A'u, where

Accuracy of an approximate static structural analysis technique based on stiffness matrix eigenmodes

Abstract: Use of the stiffness matrix eigenmodes, instead of the vibration eigenmodes, as generalized coordinates is proposed for condensation of static load deflection equations in finite element stiffness method. The modes are selected by strain energy criteria and the resulting fast, approximate analysis technique is evaluated by applications to idealized built-up wings and a fuselage segment. The best results obtained are a two-order of magnitude reduction of the number of degrees of freedom in a high aspect ratio wing associated with less than one percent error in prediction of the largest displacement.

Van frame structural evaluation

Abstract: This paper describes the structural evaluation of a van production chassis frame, a light weight frame design and four other modified production frames. Static structural properties were determined by a combination of laboratory joint stiffness measurements and a finite element model incorporating empirical stiffness values. The finite element analysis results are compared to laboratory frame bending and torsion measurements.

Stability Analysis of Cable-Stayed Rigid Frames

Abstract: The stability analysis of two-dimensional cable-stayed rigid frames containing a mixture of rigid and pin joints, may be conveniently performed on the computer to obtain the critical buckling load and its associated mode shape. The two-dimensional frame may contain a mixture of rigid and pin joints, as well as a mixture of members under combined bending and axial force and cables under axial force only. The primary state under the critical buckling load may be a deformed state by itself, to which the buckling mode shape is superimposed. The displacement method is used to establish the global stiffness matrix. The effects of the primary axial forces on the stiffness coefficients in bending and on the member equilibrium by their separate lines of action are both considered. The buckling load factor is obtained by raising the relative primary axial forces until the determinant of the global stiffness matrix becomes zero. Higher modes may be obtained by further increasing the relative primary axial forces.

Analysis of Partially Uplifted Base Mats

Abstract: This is a systematic method of analyzing a partially uplifted base mat on an elastic foundation, without removing tensile soil springs. The initial system stiffness matrix is used throughout the operation. The method becomes beneficial and important when the size of the system stiffness matrix of a finite element model is relatively large and many loading conditions cause the mat to be uplifted partially in different ways. The generalized equilibrium equations can be incorporated with general structural analysis computer programs, such as STRUDL, SAP, etc.

A Simplified Method for Elastic-Plastic Analysis of Plate Structure by the Finite Element Method (The 1 st Report)

Abstract: The present paper proposes a methed for the elastic-plastic analysis of plate bending problems using the finite element method. In the present method plastic deformations are idealized according to the concept of plastic hinge lines, while the conventional finite element procedure is employed before yielding occurs. Morley's plate bending element is used herein because of its simplicity. Plastic analysis is based on the assumption that plastic bending deformations are concentrated in plastic hinges along the element boundaries. In order to decrease dependancy of calculated results on mesh idealization, simple automatic mesh re-subdivision is implemented in the procedure.This method overcomes the following two difficulties in the ordinary finite element method; time consuming numerical integration of stiffness matrix along plate thickness and overestimation of stiffness due to shape functions with too strong compatibility conditions for localized plastic deformations.Basic numerical examples are studied to verify the validity of the present method.

Algebraic Properties of the Global Matrices

Abstract: The chapter presents the spectral norms of K and M to find a nontrivial lower bound on the smallest eigenvalue of K to establish the positive definiteness of the global stiffness matrix. The refinement of the mesh, intended to improve the discretization accuracy, invariably causes the condition of the global stiffness matrix K to decline. The chapter discusses the symmetry of Green's function that depends on differential equation and boundary conditions. Boundary value problems for which Green's function is symmetric are termed symmetric or self-adjoint. Symmetry or self-adjointness is an intrinsic property of the boundary value problem that is preserved in the finite element discretization. The chapter also describes positive flexibility matrices. A matrix whose entries are all positive is said to be positive. Some global stiffness matrices generated by finite elements for second-order problems possess positive inverses or flexibility matrices. The chapter presents methods like Gauss elimination that create computational errors in the solution comparable in magnitude to those occurring initially when the data are stored. Fourth-order problems give rise to stiffness matrices that become ill conditioned at a faster rate than those arising in second-order problems.