Showing papers on "Direct stiffness method published in 1980"
Book•
01 Jan 1980
TL;DR: In this paper, the Flexibility Method for Framed Structures is presented, along with a detailed analysis of the stiffness matrix of the members of a plane truss and their corresponding rigidness matrix.
Abstract: 1 Basic Concepts of Structural Analysis.- 1.1 Introduction.- 1.2 Types of Framed Structures.- 1.3 Deformations in Framed Structures.- 1.4 Actions and Displacements.- 1.5 Equilibrium.- 1.6 Compatibility.- 1.7 Static and Kinematic Indeterminacy.- 1.8 Structural Mobilities.- 1.9 Principle of Superposition.- 1.10 Action and Displacement Equations.- 1.11 Flexibility and Stiffness Matrices.- 1.12 Equivalent Joint Loads.- 1.13 Energy Concepts.- 1.14 Virtual Work.- References.- Problems.- 2 Fundamentals of the Flexibility Method.- 2.1 Introduction.- 2.2 Flexibility Method.- 2.3 Examples.- 2.4 Temperature Changes, Prestrains, and Support Displacements.- 2.5 Joint Displacements, Member End-Actions, and Support Reactions.- 2.6 Flexibilities of Prismatic Members.- 2.7 Formalization of the Flexibility Method.- Problems.- 3 Fundamentals of the Stiffness Method.- 3.1 Introduction.- 3.2 Stiffness Method.- 3.3 Examples.- 3.4 Temperature Changes, Prestrains and Support Displacements.- 3.5 Stiffness of Prismatic Members.- 3.6 Formalization of the Stiffness Method.- Problems.- 4 Computer-Oriented Direct Stiffness Method.- 4.1 Introduction.- 4.2 Direct Stiffness Method.- 4.3 Complete Member Stiffness Matrices.- 4.4 Formation of Joint Stiffness Matrix.- 4.5 Formation of Load Vector.- 4.6 Rearrangement of Stiffness and Load Arrays.- 4.7 Calculation of Results.- 4.8 Analysis of Continuous Beams.- 4.9 Example.- 4.10 Plane Truss Member Stiffnesses.- 4.11 Analysis of Plane Trusses.- 4.12 Example.- 4.13 Rotation of Axes in Two Dimensions.- 4.14 Application to Plane Truss Members.- 4.15 Rotation of Axes in Three Dimensions.- 4.16 Plane Frame Member Stiffnesses.- 4.17 Analysis of Plane Frames.- 4.18 Example.- 4.19 Grid Member Stiffnesses.- 4.20 Analysis of Grids.- 4.21 Space Truss Member Stiffnesses.- 4.22 Selection of Space Truss Member Axes.- 4.23 Analysis of Space Trusses.- 4.24 Space Frame Member Stiffnesses.- 4.25 Analysis of Space Frames.- Problems.- 5 Computer Programs for Framed Structures.- 5.1 Introduction.- 5.2 FORTRAN Programming and Flow Charts.- 5.3 Program Notation.- 5.4 Preparation of Data.- 5.5 Description of Programs.- 5.6 Continuous Beam Program.- 5.7 Plane Truss Program.- 5.8 Plane Frame Program.- 5.9 Grid Program.- 5.10 Space Truss Program.- 5.11 Space Frame Program.- 5.12 Combined Program for Framed Structures.- References.- 6 Additional Topics for the Stiffness Method.- 6.1 Introduction.- 6.2 Rectangular Framing.- 6.3 Symmetric and Repeated Structures.- 6.4 Loads Between Joints.- 6.5 Automatic Dead Load Analysis.- 6.6 Temperature Changes and Prestrains.- 6.7 Support Displacements.- 6.8 Oblique Supports.- 6.9 Elastic Supports.- 6.10 Translation of Axes.- 6.11 Member Stiffnesses and Fixed-End Actions from Flexibilities.- 6.12 Nonprismatic Members.- 6.13 Curved Members.- 6.14 Releases in Members.- 6.15 Elastic Connections.- 6.16 Shearing Deformations.- 6.17 Offset Connections.- 6.18 Axial-Flexural Interactions.- 6.19 Axial Constraints in Frames.- References.- Problems.- 7 Finite-Element Method for Framed Structures.- 7.1 Introduction.- 7.2 Stresses and Strains in Continua.- 7.3 Virtual-Work Basis of Finite-Element Method.- 7.4 One-Dimensional Elements.- 7.5 Application to Framed Structures.- References.- General References.- Notation.- Appendix A. Displacements of Framed Structures.- A.1 Stresses and Deformations in Slender Members.- A.2 Displacements by the Unit-Load Method.- A.3 Displacements of Beams.- A.4 Integrals of Products for Computing Displacements.- References.- Appendix B. End-Actions for Restrained Members.- Appendix C. Properties of Sections.- Appendix D. Computer Routines for Solving Equations.- D.1 Factorization Method for Symmetric Matrices.- D.2 Subprogram FACTOR.- D.3 Subprogram SOLVER.- D.4 Subprogram BANFAC.- D.5 Subprogram BANSOL.- References.- Appendix E. Solution without Rearrangement.- Answers to Problems.- Order Form for Diskette.
157 citations
TL;DR: In this article, the convergence requirements for a finite element may be written as a set of linear constraints on the stiffness matrix, and then a best possible stiffness matrix is constructed by constructing a stiffness matrix from the constraint equations.
Abstract: It is shown how the convergence requirements for a finite element may be written as a set of linear constraints on the stiffness matrix. It is then attempted to construct a best possible stiffness matrix. The constraint equations restrict the way in which these stiffness terms may be chosen; however, there is normally still room for improving or optimizing an element. It is demonstrated how an element stiffness matrix may be found using rigid body, constant strain and higher order deformation modes. Further, it is shown how the constraint equations may be exploited in deriving an ‘energy orthogonality theorem’. This theorem opens the door to a whole new class of simple finite elements which automatically satisfy the convergence requirements. Examples of deriving plane stress and plate bending elements are given.
78 citations
TL;DR: In this article, a procedure of deriving stiffness matrices for finite elements based on the patch-test using the natural method is described, which is tested on the construction of a triangular plate-bending element TRUNC, the natural stiffness of which appears as a simple hyperdiagonal matrix.
41 citations
TL;DR: In this article, a contact stiffness matrix for finite element analysis is defined and applied to all types of finite elements and can easily model elastic foundations supporting beam, plate or solid elements.
29 citations
TL;DR: In this article, a coated fabric element is modelled by a stable geometrically nonlinear space truss and the problem formulated using matrix structural analysis is determined by solving the system's equations using the secant method.
15 citations
TL;DR: In this paper, a tangent stiffness matrix for each element is established, which can be used for static crush analysis of structural components by setting the mass matrix zero, and the modified program has the capability to analyze structures with arbitrarily large rotation.
14 citations
TL;DR: In this article, a numerical method for the analysis of three-dimensional frames loaded dynamically into the inelastic range is developed, where the elasto-plastic force-deformation behaviour at the ends of the frame members is represented by an equation which corresponds essentially to the inverse of the Ramberg-Osgood representation.
11 citations
TL;DR: In this paper, a numerical computer method using planar flexural finite line element for the determination of buckling loads of beams, shafts and frames supported by rigid or elastic bearings is presented.
9 citations
01 Aug 1980
TL;DR: In this article, a method of vibration analysis for determining the fundamental resonant frequency and mode shape of beams and simple frames is presented, which is applicable for structures made from materials possessing a linear moment curvature relationship over the range of structural deformations considered.
Abstract: This paper presents a method of vibration analysis for determining the fundamental resonant frequency and mode shape of beams and simple frames. The method of analysis is applicable for structures made from materials possessing a linear moment curvature relationship over the range of structural deformations considered. Calculation can be performed using desk top calculators without the need to access digital computers with sophisticated programming capabilities. Vibration functions are determined for each element of the structure, linearised and added to form the dynamic stiffness matrix for the structure. The analogy of the linearised dynamic stiffness matrix is made with the static stiffness matrix used in the stiffness method of structural analysis. The linearisation technique is used to aid in the solution of the eigenvalue problem and is discussed in detail. Iterations may be required to converge to the resonant frequency of the desired accuracy. The use of the vibration functions and method of analysis is illustrated by a comprehensive example worked in full and compared with the results of a steel frame under test.
9 citations
TL;DR: In this article, a theoretical approach is analyzed of the dynamic response of pile-supported frame foundations of turbomachineries to rotor unbalances, including dynamic interaction of soil, piles, flexible foundation mat, three-dimensional structural frame, flexible rotor, and viscoelastic oil film in journal bearings.
Abstract: A theoretical approach is analyzed of the dynamic response of pile-supported frame foundations of turbomachineries to rotor unbalances. The approach includes dynamic interaction of soil, piles, flexible foundation mat, three-dimensional structural frame, flexible rotor, and viscoelastic oil film in journal bearings. The approach employs substructuring, dynamic stiffness method, and finite elements. Shear deformations and material damping are included in the stiffness matrices of the finite elements that are complex and frequency dependent. The stiffness matrix of the element is generalized to incorporate the stiffness and damping of the supporting medium including piles. It was found that soil-structure interaction markedly affects the response of the frame as well as the rotors in the lowest resonant regions. In the vicinity of a high operating speed, soil-structure interaction can be neglected.
9 citations
01 Jan 1980
TL;DR: In this paper, the main feature of this second edition is a new chapter on elastic behaviour and design, and new sections on the analysis of two pinned arches, the use of instantaneous centres, and on ideas of symmetry and anti-symmetry in moment distribution.
Abstract: This book is primarily concerned with structures in the linear elastic range of behaviour. The main feature of this second edition is a new chapter on elastic behaviour and design. There are also new sections on the analysis of two pinned arches, the use of instantaneous centres, and on ideas of symmetry and anti-symmetry in moment distribution. In addition, all the problems have been recast in SI units. The book contains the following chapters: definitions and introductory concepts; statically determinate plane structures; space statics and determinate space structures; basic structural concepts; stiffness and flexibility; moment distribution; matrix stiffness method; instability of struts and frameworks; structural dynamics; elasticity problems and the finite difference method; the finite element method; computer application; plastic theory of structures. The ISBN of the hardback version of this book is 0-17-761061-1. (TRRL)
TL;DR: Several methods based on a finite element stiffness formulation developed in the last few years to obtain solutions to elastic-plastic problems involving small deformations are reviewed in this paper, where specific attention is drawn to the successful use of the Tresca yield condition.
Abstract: Several methods based on a finite element stiffness formulation developed in the last few years to obtain solutions to elastic-plastic problems involving small deformations are reviewed in this paper. Various yield conditions, i.e., von Mises, Tresca, and Approximate Tresca, that have frequently been employed in the development of the plastic stress-strain relations in the incremental form, are presented. Specific attention is drawn to the successful use of the Tresca yield condition. Two solution techniques, i.e., direct stiffness method and quadratic programming technique, are compared in terms of their computational efficiency. Iterative and interpolative schemes that are utilized in an incremental plastic analysis to satisfy the yield condition are given. Comparisons of solutions using constant strain and linear strain triangular elements are presented indicating the advantages of one over the other. A joint application of the substructuring and mesh-refinement schemes in elastic-plastic finite element analysis is demonstrated.
TL;DR: In this article, the authors deal with the nonlinear creep analysis using equilibrium finite elements, adopting a concept of the mean value of the equivalent shear modulus, a direct iterative procedure is proposed with the minimum calculation in the modification of the global stiffness matrix.
Abstract: The paper deals with the nonlinear creep analysis using equilibrium finite elements. In adopting a concept of the mean value of the equivalent shear modulus, a direct iterative procedure is proposed with the minimum calculation in the modification of the global stiffness matrix. The difficulties due to the incompressibility of the creep flow are overcome by a numerical artifice where the hydrostatic stress component is considered as a Lagrange parameter. Some numerical results are shown and compared with the analytical method.