Explicit expressions for triangular torus element stiffness matrix.
Explicit expressions for stiffness matrix of triangular torus elements associated with linear displacement fields and generalized Hookian material
Utku, S.↗
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Accuracy of an approximate static structural analysis technique based on stiffness matrix eigenmodes
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.
Sobieszczanski-Sobieski, J.↗
Derivatives of a statically reduced stiffness matrix with respect to sizing variables
An expression is obtained for the first derivatives with respect to the sizing variables of a statically reduced stiffness matrix that is a nonlinear function of the sizing variables, where the unreduced stiffness matrix is a linear function of the sizing variables. An accepted procedure to reduce the number of degrees of freedom is to eliminate a number of nodal displacements from the degrees of freedom such that the accuracy of the flutter analysis is not significantly affected. In a typical optimization procedure with flutter constraints, the derivative of the stiffness matrix may be used in a form that contains the characteristic vector of the flutter matrix equation and the transpose of the characteristic vector of the adjoint flutter matrix equation corresponding to a particular solution of the flutter equation.
Oconnell, R. F.↗
A new pre-loaded beam geometric stiffness matrix with full rigid body capabilities
Space structures, such as the Space Station solar arrays, must be extremely light-weight, flexible structures. Accurate prediction of the natural frequencies and mode shapes is essential for determining the structural adequacy of components, and designing a controls system. The tension pre-load in the 'blanket' of photovoltaic solar collectors, and the free/free boundary conditions of a structure in space, causes serious reservations on the use of standard finite element techniques of solution. In particular, a phenomenon known as 'grounding', or false stiffening, of the stiffness matrix occurs during rigid body rotation. The authors have previously shown that the grounding phenomenon is caused by a lack of rigid body rotational capability, and is typical in beam geometric stiffness matrices formulated by others, including those which contain higher order effects. The cause of the problem was identified as the force imbalance inherent in the formulations. In this paper, the authors develop a beam geometric stiffness matrix for a directed force problem, and show that the resultant global stiffness matrix contains complete rigid body mode capabilities, and performs very well in the diagonalization methodology customarily used in dynamic analysis.
Bosela, P. A.↗
Computer program performs stiffness matrix structural analysis
Computer program generates the stiffness matrix for a particular type of structure from geometrical data, and performs static and normal mode analyses. It requires the structure to be modeled as a stable framework of uniform, weightless members, and joints at which loads are applied and weights are lumped.
Bamford, R.↗
Generalized stiffness matrix of a curved-beam element
Stiffness matrix derivation for curved beam emphasizing uncoupled normal to plane loads
Lee, H.-P.↗
Generalized ring stiffness matrix for ring- stiffened shells of revolution
Generalized ring stiffness matrix for ring stiffened shells of revolution
Walz, J. E.↗
Stiffness matrix for a triangular sandwich element in bending
Triangular finite sandwich element for direct stiffness matrix determination of bending in plates and shells
SANDWICH PLATE↗
Stiffness matrix solution for shells of revolution possessing variable thickness heat protection
Stiffness matrix solution for shells of revolution possessing variable thickness heat protection
TOROIDAL SHELL↗
Effect of curvature on extensional stiffness matrix of 2-D braided composite tubes
In the micromechanical analysis of braided composite tubes, the effects of curvature are often ignored. This approach is acceptable for thin-walled tubes with a large radius. However, in case of small diameter thick-walled tubes, such an approach may lead to inaccurate results. Therefore, it is of interest to determine when the curvature effects of tubular geometry become important in micromechanics. In this study, the extensional stiffness matrix of 2-D braided composite tubes was calculated using a curved unit-cell. The periodicity was imposed in circumferential and longitudinal directions of the tube. The extensional stiffness coefficients were calculated by simulating an internal pressure test, uniaxial tensile test, and torsion test. The obtained stiffness coefficients were compared to those obtained using a flat unit-cell. The results of curved unit-cell were different from that of flat unit-cell. The differences in stiffness coefficients, calculated using curved and flat unit cells were as high as 13%.
42 ENGINEERING↗
Evaluation of Extensional Stiffness Matrix [A]. of Braided Composite Tubes
A novel method for analyzing tubular textile composites was developed by obtaining a curved repeatable unit cell (RUC) from the transformation of a flat RUC. Periodic boundary conditions were imposed on the tubular RUC. The stiffness matrix of the composite was then evaluated using transversely isotropic yarn and isotropic matrix. It was found that the stiffness coefficients A11, A12 of the composite are more sensitive to a change in the radius of the composite compared to A22 and A66.
Thandaga Nagaraju, Hematnh↗
Generalization of rectangular element stiffness matrix and thermal load vector associated with a(0) + a(1)x + a(2)y + a(3)xy type interpolation rule
The stiffness-matrix formulation for the rectangular finite element described by Melosh (1963) and Weaver and Johnston (1984) is generalized to orthotropic materials with material axes not necessarily coincident with the x and y axes; i.e., the condition d(13) = d(23) = 0 is removed. Also included are explicit expressions for the element load vector associated with nonuniform temperature increase in the element. Applications to the analysis of thermal stresses in thin Si-crystal ribbons subjected to temperature changes with highly nonuniform lengthwise and transverse gradients (Utku et al., 1986) and to the simulation of the thermoviscoelastic behavior of growing Si ribbons (Utku and Ray, 1986) are indicated.
Ray, Sujit K.↗
Finite-element grid improvement by minimization of stiffness matrix trace
A new and simple method of finite-element grid improvement is presented. The objective is to improve the accuracy of the analysis. The procedure is based on a minimization of the trace of the stiffness matrix. For a broad class of problems this minimization is seen to be equivalent to minimizing the potential energy. The method is illustrated with the classical tapered bar problem examined earlier by Prager and Masur. Identical results are obtained.
Kittur, Madan G.↗
Finite-element grid improvement by minimization of stiffness matrix trace
A new and simple method of finite-element grid improvement is presented. The objective is to improve the accuracy of the analysis. The procedure is based on a minimization of the trace of the stiffness matrix. For a broad class of problems this minimization is seen to be equivalent to minimizing the potential energy. The method is illustrated with the classical tapered bar problem examined earlier by Prager and Masur. Identical results are obtained.
Kittur, Madan G.↗
A Study of the Effect of Adhesive and Matrix Stiffnesses on the Axial, Normal, and Shear Stress Distributions of a Boron-epoxy Reinforced Composite Joint
The mechanical properties of a symmetrical, eight-step, titanium-boron-epoxy joint are discussed. A study of the effect of adhesive and matrix stiffnesses on the axial, normal, and shear stress distributions was made using the finite element method. The NASA Structural Analysis Program (NASTRAN) was used for the analysis. The elastic modulus of the adhesive was varied from 345 MPa to 3100 MPa with the nominal value of 1030 MPa as a standard. The nominal values were used to analyze the stability of the joint. The elastic moduli were varied to determine their effect on the stresses in the joint.
Howell, W. E.↗
Stiffness-matrix condition number and shape sensitivity errors
This paper derives an error magnification index for assessing the sensitivity of the displacement field to errors in the load vector. It is shown that the error magnification index is less conservative than the stiffness-matrix condition number and that, for some cases, no error magnification occurs even when the condition number is very high. The proposed index was used to calculate the derivatives of beam response to changes in the beam structural parameters, using a semianalytical method. It is shown that the proposed index discriminates well between the calculation of the derivative with respect to length, which is very sensitive to errors, and the calculation of the derivative with respect to cross-sectional height, which is not sensitive.
Haftka, Raphael T.↗
Mesh refinement in finite element analysis by minimization of the stiffness matrix trace
Most finite element packages provide means to generate meshes automatically. However, the user is usually confronted with the problem of not knowing whether the mesh generated is appropriate for the problem at hand. Since the accuracy of the finite element results is mesh dependent, mesh selection forms a very important step in the analysis. Indeed, in accurate analyses, meshes need to be refined or rezoned until the solution converges to a value so that the error is below a predetermined tolerance. A-posteriori methods use error indicators, developed by using the theory of interpolation and approximation theory, for mesh refinements. Some use other criterions, such as strain energy density variation and stress contours for example, to obtain near optimal meshes. Although these methods are adaptive, they are expensive. Alternatively, a priori methods, until now available, use geometrical parameters, for example, element aspect ratio. Therefore, they are not adaptive by nature. An adaptive a-priori method is developed. The criterion is that the minimization of the trace of the stiffness matrix with respect to the nodal coordinates, leads to a minimization of the potential energy, and as a consequence provide a good starting mesh. In a few examples the method is shown to provide the optimal mesh. The method is also shown to be relatively simple and amenable to development of computer algorithms. When the procedure is used in conjunction with a-posteriori methods of grid refinement, it is shown that fewer refinement iterations and fewer degrees of freedom are required for convergence as opposed to when the procedure is not used. The mesh obtained is shown to have uniform distribution of stiffness among the nodes and elements which, as a consequence, leads to uniform error distribution. Thus the mesh obtained meets the optimality criterion of uniform error distribution.
Kittur, Madan G.↗
Stiffness matrix structural analysis
Computer program for stiffness of structure with lumped masses, weightless members, and many degrees of freedom - structural dynamics
COMPUTER PROGRAM↗