Showing papers on "Direct stiffness method published in 1982"
TL;DR: In this article, an approach which is concerned with the formulation of incompatible elements for solid continuum and for plate bending problems by the Hellinger-Reissner principle is presented.
Abstract: An element stiffness matrix can be derived by the conventional potential energy principle and, indirectly, also by generalized variational principles, such as the Hu-Washizu principle and the Hellinger-Reissner principle. The present investigation has the objective to show an approach which is concerned with the formulation of incompatible elements for solid continuum and for plate bending problems by the Hellinger-Reissner principle. It is found that the resulting scheme is equivalent to that considered by Tong (1982) for the construction of hybrid stress elements. In Tong's scheme the inversion of a large flexibility matrix can be avoided. It is concluded that the introduction of additional internal displacement modes in mixed finite element formulations by the Hellinger-Reissner principle and the Hu-Washizu principle can lead to element stiffness matrices which are equivalent to the assumed stress hybrid method.
181 citations
TL;DR: In this paper, the exact dynamic stiffness matrix for a straight and uniform beam element whose elastic and inertial axes are not coincident is derived for planar assemblages of connected bending-torsion beams.
98 citations
TL;DR: In this article, the elastic-plastic and plastic stiffness matrices for one-dimensional members were derived using the incremental theory of plasticity and a new method for plastic analysis of plates and solid bodies was developed.
79 citations
TL;DR: In this article, the exact stiffness matrix for a circularly curved beam subjected to loading in its own plane, derived from the governing differential equations and from the finite element procedure, is presented, the elements of the stiffness matrix being obtained explicitly, thus eliminating the need for any numerical matrix inversion procedures in the formulation of the matrix.
Abstract: The exact 6 x 6 stiffness matrix for a circularly curved beam subjected to loading in its own plane, derived from the governing differential equations and from the finite element procedure, is presented, the elements of the stiffness matrix being obtained explicitly, thus eliminating the need for any numerical matrix inversion procedures in the formulation of the matrix. The displacement transformation matrix, which allows the beam element to be incorporated into a general frameworks program is then formulated, after which the treatment of distributed loading is described. The accuracy and correctness of the stiffness and transformation matrices are verified by comparison with a range of convergent solutions obtained from subdivision of the curved members into a number of straight segments.
30 citations
TL;DR: In this article, a semi-implicit direct time integration procedure is presented which avoids factorization of the implicit difference solution matrix and requires only vectorial calculations and hence needs the same computer core space as explicit integration procedures.
Abstract: A semi-implicit direct time integration procedure is presented which avoids factorization of the implicit difference solution matrix. The procedure, if properly implemented, requires only vectorial calculations and hence needs the same computer core space as explicit integration procedures. Guidelines for splitting the stiffness matrix into upper and lower matrices are established, which among other things are designed to satisfy a correct transmission of rigid-body motions from element (or grid) to its adjacent elements.
18 citations
12 citations
TL;DR: In this paper, effective mechanical properties for large repetitive framelike structures are derived using combinations of strength of material and orthogonal transformation techniques using symmetry considerations in order to identify independent property constants.
12 citations
TL;DR: In this article, a finite segment method is applied to solve biaxially loaded reinforced concrete columns, where the column is treated as a space structure after segmentation, and the sections are divided into finite elements of steel and concrete in order to calculate its tangent stiffnesses properties at different levels of strain.
Abstract: The finite segment method is applied here to solve biaxially loaded reinforced concrete columns. The column is treated as a space structure after segmentation. The sections are divided into finite elements of steel and concrete in order to calculate its tangent stiffnesses properties at different levels of strain. The segment stiffness relationship is computed by solving the governing differential equations about the principal axes of the cross section. Direct stiffness method is utilized to construct the whole column stiffness matrix (master stiffness matrix). Nonlinearities due to material plasticity and geometrical change are handled by an iterative procedure based on the modified tangent stiffness approach. Comparisons of failure load and deflection with biaxially loaded reinforced concrete column tests show an excellent correlation between theory and test data.
12 citations
TL;DR: In this article, a finite element implementation of the virtual-work principle using the method of local jacobian derivative is proposed and a direct way to compute stiffness is also given.
10 citations
TL;DR: In this article, the stiffness matrix for a structural member is obtained using the differential equations derived by V.Z. Vlasov, and the presence of additional off-diagonal elements over the conventional tridiagonal form is observed.
Abstract: Stiffness matrix for a structural member is obtained using the differential equations derived by V.Z. Vlasov. Presence of additional off-diagonal elements over the conventional tridiagonal form is observed. A number example is shown in order to compare the relative magnitudes of elements in the stiffness matrix and some of the new off-diagonal elements are found to be of considerable importance. This stiffness matrix conclusively demonstrates the inter-relationship between the three rotational degrees of freedom. This coupling is found to reduce the value of the critical axial force below all three individual buckling loads, viz: lateral buckling about major and minor axes and torsional buckling. All these effects are attributed to an internal force called as “bimoment’.
TL;DR: In this article, the application of the infinite element method to two-dimensional magnetic field problems is described, where the system stiffness matrix is derived using the variational method, while boundary conditions at the interfaces of finite element regions and infinite element regions are dealt with using collocation method and modified variational methods.
Abstract: This paper describes the applications of the infinite element method to two‐dimensional magnetic field problems. The system stiffness matrix is derived using the variational method, while boundary conditions at the interfaces of finite element regions and infinite element regions are dealt with using collocation method and modified variational method. The method is applied to two simple linear problems, and the results are compared with the analytic solutions. It is observed that the numerical solutions are in good agreement with the analytic solutions. It is also observed that the proposed method gives more accurate results than the standard finite element method.
TL;DR: In this article, the authors used the techniques of discrete field analysis to investigate the response of X-braced trusses to various static loading conditions, and derived stiffness coefficients which comprise the equivalent beam element stiffness matrix.
Abstract: The techniques of discrete field analysis are utilized to investigate the response of X-braced trusses to various static loading conditions. Deflection formulas for arbitrary static loads are presented in finite Fourier series form. These formulas are used to derive stiffness coefficients which comprise the equivalent beam element stiffness matrix for a given X-braced truss. Fixed end moments for arbitrary static loads are also derived from the deflection formulas. All stiffness formulas are exact in the context of linear, elastic truss analysis and are valid for an arbitrary number of panels. These stiffness coefficients when compared to approximate estimates are found to vary by as much as 100% within a given range of span lengths. The formulas can be used to analyze a variety of structural systems which have X-braced trusses as the basic component. Examples include two-way truss systems, trussed frames, and planar trusses continuous over several supports. The analysis of such systems would be identical to that in which the individual components were beams except that here modified stiffness coefficients would be used.
01 Jan 1982
TL;DR: In this article, a boundary element formulation for elastostatic problems is presented, which is expressed in terms of the matrix notation, so that it is easily applicable to an available system of matrix structural analysis.
Abstract: This paper presents a boundary element formulation for elastostatic problems. The formulation is expressed in terms of the matrix notation, so that it is easily applicable to an available system of matrix structural analysis. A computer program developed is used to calculate the stress intensity factor KI for some example problems in plane elasticity. Comparison is made between the boundary element calculations and other solutions, whereby the effectiveness of the boundary element method is demonstrated.
TL;DR: In this paper, the identification of the mass, damping and stiffness matrix for the finite-element formulation of a structure was given, and the quadrature integration procedure was used to find the desired matrices when reasonable assumptions hold.
Abstract: The identification of the mass, damping and stiffness matrix for the finite-element formulation of a structure will be given. It will be shown that the quadrature integration procedure can be used to find the desired matrices when reasonable assumptions hold. The mass, damping and stiffness matrices of the matrix polynomial are identified by the algorithm.
TL;DR: In this article, the use of numerical and closed form integration in computation of element stiffness matrices for axisymmetric finite element analysis is compared with an exact solution obtained from classical methods.
Abstract: This note compares the use of numerical and closed form integration in computation of element stiffness matrices for axisymmetric finite element analysis. Only constant strain elements are considered. Results obtained with Gaussian quadrature and closed form integrators are compared mutually and with an exact solution obtained from classical methods. The FEM global equations estimate the force-displacement behaviour of an elastic continuum with an accuracy that depends on the integration method used. Selection of an integration order minimizing error is particularly critical in the presence of high stress gradients. Best results in the vicinity of the axis of revolution may be obtained with single-point integration rather than higher order approximations or exact integration of the element stiffness matrix. This phenomenon and its consequences are subsequently discussed.
01 Dec 1982
TL;DR: In this article, a tester was designed capable of controlling the bearing axial preload, speed, and rotor unbalance, and the results of extensive testing were used to verify analytical predictions, increase confidence in existing bearing computer programs, and to serve as a data base for efforts to correct these programs.
Abstract: The dynamic radial stiffness characteristics of rolling element bearings are currently determined by analytical methods that have not been experimentally verified. These bearing data are vital to rotating machinery design integrity because accurate critical speeds and rotor stability predictions are highly dependent on the bearing stiffness. A tester was designed capable of controlling the bearing axial preload, speed, and rotor unbalance. The rotor and support structures were constructed to permit critical speeds that are predominantly determined by a 57 mm test bearing. A curve of calculated critical speed versus stiffness was used to determine the actual bearing stiffness from the empirical data. The results of extensive testing are used to verify analytical predictions, increase confidence in existing bearing computer programs, and to serve as a data base for efforts to correct these programs.
TL;DR: In this paper, a direct vector combination procedure is developed for the formulation of finite element stiffness matrices, where only the homogeneous solution modes to governing equations of a problem and a uniquely defined interpolation displacement function along the element boundary are used to generate pairs of nodal displacement and nodal force vectors.
Abstract: A direct vector combination procedure is developed for the formulation of finite element stiffness matrices. Only the homogeneous solution modes to governing equations of a problem and a uniquely defined interpolation displacement function along the element boundary are used to generate pairs of nodal displacement and nodal force vectors. The stiffness matrix is obtained by a simple multiplication of the nodal displacement and nodal force vectors. The element formed passes all the higher order patch tests for the order of solution modes included in the formulation. However, the stiffness matrix may become unsymmetrical. Restoring symmetry leads to compromising some of the higher order patch test performances. The present procedure is shown to have direct relations to those of the displacement model and the hybrid stress model. The present procedure presents new possibilities for the improvement of element performance. The procedure itself can also be used to study the limitations of element behaviour.
01 Oct 1982
TL;DR: In this article, a finite element model that is suitable for the static analysis of shells of revolution with arbitrary local deviations is presented, and the form of the global stiffness matrix resulting when different forms of nodal degrees of freedom are combined is illustrated.
Abstract: A finite element model that is suitable for the static analysis of shells of revolution with arbitrary local deviations is presented. The model employs three types of elements: rotational, general, and transitional shell elements. The rotational shell elements are used in the region where the shell is axisymmetric. The general shell element are used in the local region of the deviation. The transitional shell elements connect these two distinctively different types of elements and make it possible to combine them in a single analysis. The form of the global stiffness matrix resulting when different forms of nodal degrees of freedom are combined is illustrated. The coupling of harmonic degrees of freedom due to the locally nonaxisymmetric geometry was studied. The use of a substructuring technique and separate partial harmonic analysis is recommended.
TL;DR: In this article, a finite element static analysis of the structure is performed using approximate stiffness coefficients, which are determined by successive iterations by comparing some of the computed displacements to measured displacements.
Abstract: A Newton-Raphson method combined with a weighted least square technique using experimental data (measured displacements) is developed in order to determine the stiffness coefficients of elastic composite materials. A finite element static analysis of the structure is performed using approximate stiffness coefficients. The exact coefficients are determined by successive iterations by comparing some of the computed displacements to measured displacements.Preliminary tests indicate that this technique is useful for predicting the appropriate experimental conditions.Secondly, the procedure converges rapidly, even for very poor starting ap proximations of the stiffness coefficients, provided the loading conditions are favorable.Finally, the technique reveals to be sensitive to measurement errors despite the use of a weighting factor in the least square technique.