Showing papers on "Direct stiffness method published in 1975"
TL;DR: In this article, the basic idea is brought to a logical conclusion by the direct construction of the factorised form of the elemental and overall stiffness matrices from their natural stiffness roots, denoted as the natural factor formulation.
52 citations
TL;DR: Zienkiewicz, O C and Cheung, Y K, The Finite Element Method in Structural and Continuum Mechanics, McGraw-Hill, London, 1967, p 66 as mentioned in this paper.
Abstract: References 1 Melosh, R J, "Basis for Derivation of Matrices for the Direct Stiffness Method," AIAA Journal, Vol 1, No 7, July 1963, pp 16311637 2 Oden, J T, Finite Elements of Nonlinear Continua, McGraw-Hill, New York, 1972, p 146 3 Przemieniecki, J S, Theory of Matrix Structural Analysis, McGraw-Hill, New York, 1968, pp 83-106 4 Turner, M J, Clough, R W, Martin, H C, and Topp, L J, ""Stiffness and Deflection Analysis of Complex Structures," Journal of the Aeronautical Sciences, Vol 23, 1956, pp 805-823 5 Wilson, E L, Taylor, R L, Doherty, W P, and Ghabousii, J, "'Incompatible Displacement Models," Numerical and Computer Methods in Structural Mechanics, edited by S J Fenves et al Academic Press, New York, pp 43-57 6 Zienkiewicz, O C and Cheung, Y K, The Finite Element Method in Structural and Continuum Mechanics, McGraw-Hill, London, 1967, p 66
36 citations
TL;DR: In this article, the general stiffness matrix for a beam element is derived from the Bernoulli-Euler differential equation with the inclusion of axial forces, and the terms of this matrix are expanded into a power series as a function of the two variables: the axial force, and; the vibrating frequency.
Abstract: The general stiffness matrix for a beam element is derived from the Bernoulli–Euler differential equation with the inclusion of axial forces. The terms of this matrix are expanded into a power series as a function of the two variables: the axial force, and; the vibrating frequency. It is shown that the first three terms of the resulting series, which are derived in the technical literature from assumed static displacement functions, correspond respectively to the elastic stiffness matrix, the consistent mass matrix, and the geometric matrix. Higher order terms up to the second order terms of the series expansion are obtained explicitly. Also a discussion is presented for establishing the region of convergence of the series expansion for the dynamic stiffness matrix, the stability matrix, and the general stiffness matrix.
27 citations
TL;DR: The variational principle and the corresponding finite element formulation, which allows the standard direct stiffness method of structural analysis to be used, are discussed in this article, and convergence criteria and bounds for the direct flexibility-influence coefficient are examined.
Abstract: Alternate hybrid stress finite element models in which the internal equilibrium equations are satisfied on the average only, while the equilibrium equations along the interelement boundaries and the static boundary conditions are adhered to exactly a priori, are developed. The variational principle and the corresponding finite element formulation, which allows the standard direct stiffness method of structural analysis to be used, are discussed. Triangular elements for a moderately thick plate and a doubly-curved shallow thin shell are developed. Kinematic displacement modes, convergence criteria and bounds for the direct flexibility-influence coefficient are examined.
18 citations
01 Jan 1975
TL;DR: The paper presents a new numerical solution procedure of the quadratic matrix equations, based on a combined Sturm sequence and inverse iteration technique enabling economical and accurate determination of a few required eigenvalues and associated vectors.
Abstract: This paper is concerned with the efficient and accurate solution of the eigenvalue problem represented by quadratic matrix equations. Such matrix forms are obtained in connection with the free vibration analysis of structures, discretized by finite 'dynamic' elements, resulting in frequency-dependent stiffness and inertia matrices. The paper presents a new numerical solution procedure of the quadratic matrix equations, based on a combined Sturm sequence and inverse iteration technique enabling economical and accurate determination of a few required eigenvalues and associated vectors. An alternative procedure based on a simultaneous iteration procedure is also described when only the first few modes are the usual requirement. The employment of finite dynamic elements in conjunction with the presently developed eigenvalue routines results in a most significant economy in the dynamic analysis of structures.
17 citations
TL;DR: In this article, the stiffness coefficients corresponding to the 0th, 1st, and n th harmonics are presented in closed form, which can be readily coded into any special or general purpose structural analysis computer program, represent the exact solution to any structural model consisting of nodal displacements and forces.
15 citations
6 citations
TL;DR: In this article, the authors developed an effective method for the ultimate strength analysis of large size structures, named as Idealized Structural Unit Method (I-SUM), which is applied to double bottom structures.
Abstract: In a previous paper, two of the authors have developed an effective method for the ultimate strength analysis of large size structures. The method is named as “Idealized Structural Unit Method”.In the method, a large size element with idealized nonlinear character was necessary and an example element, “Girder Element”, was developed. In this paper, this method is applied to double bottom structures. The state of two-dimensional stress in the tank top and the bottom shell plating is considered. Conditions for buckling of these plates are established and its post buckling stiffness is determined. The condition for their ultimate strength and stiffness at the ultimate strength are determined in connection with the girder element.An example structure is analysed and the results of the analysis are presented.
3 citations
TL;DR: In this article, a direct iterative numerical method is presented for predicting the post-local-buckling response of thin-walled continuous structures, where nonlinearities due to local buckling and nonlinear material properties are accounted for by the nonlinear moment-curvature relations of the section derived with the aid of effective width concept.
2 citations
01 Sep 1975
TL;DR: In this article, a survey of current improvements to the program is presented which includes static analysis with differential stiffness rigid format, normal modes with differential stiff format, the TRIAAX and TRAPAX elements, the CNGRNT feature, fully stressed design, element strain energy and grid point force balance, and complex modal displacement plots.
Abstract: Several improvements and capabilities were developed and installed in intermediate levels and are being analyzed and evaluated. A survey of current improvements to the program is presented which includes static analysis with differential stiffness rigid format, normal modes with differential stiffness rigid format, the TRIAAX and TRAPAX elements, the CNGRNT feature, fully stressed design, element strain energy and grid point force balance, and complex modal displacement plots.
01 Sep 1975
TL;DR: In this paper, the differential stiffness of a triangular solid of revolution elements is derived for the case of rigid body rotation only, the rotation being about the circumferential axis of a pneumatic tire.
Abstract: The derivation is presented of the differential stiffness for triangular solid of revolution elements. The derivation takes into account the element rigid body rotation only, the rotation being about the circumferential axis. Internal pressurization of a pneumatic tire is used to illustrate the application of this feature.