Senol Utku

FINITE ELEMENT ANALYSIS OF ELASTIC–PLASTIC FIBROUS COMPOSITE STRUCTURES

Abstract A three dimensional finite element code has been developed for the elastic-plastic analysis of fiber-reinforced composite materials and structures. The geometry, constitutive equations, and stiffness relations of the continuum element representing the composite are described. The finite element solution is obtained in the context of the displacement method of analysis. Solution of the nonlinear equilibrium equations is obtained with a Newton-Raphson type iteration technique. Results obtained using the finite element program for uniaxial loading of composite laminates show agreement with experiments. Other results for laminates describing development of plastic zones and overall stress-strain response are also shown for two problems: a plate with a hole and a notched plate.

Vibration Suppression for Large Scale Adaptive Truss Structures Using Direct Output Feedback Control1

In this article, the vibration control of adaptive truss structures, where the control actuation is provided by length adjustable active members, is formulated as a direct output feedback control problem. A control method named Model Truncated Output Feedback (MTOF) is presented. The method allows the control feedback gain to be determined in a decoupled and truncated modal space in which only the critical vibration modes are retained. The on-board computation required by MTOF is minimal; thus, the method is favorable for the applications of vibration control of large scale structures. The truncation of the modal space inevitably introduces spillover effect during the control process. In this article, the effect is quantified in terms of active member locations, and it is shown that the optimal placement of active members, which minimizes the spillover effect (and thus, maximizes the control performance), can be sought. The problem of optimally selecting the locations of active members is also treated.

Errors in reduction methods

Abstract A mathematical basis is given for comparing the relative merits of various techniques used to reduce the order of large linear and non-linear dynamics problems during their numerical integration. In such techniques as Guyan-Irons, path derivatives, selected eigenvectors, Ritz vectors, etc., the nth order initial value problem of [ /.y = f(y) for t > 0, y(0) given] is typically reduced to the mth order (m ⪡ n) problem of z = g(z) for t > 0, z(0) given] by the transformation y = Pz where P changes from technique to technique. This paper gives an explicit approximate expression for the reduction error ei in terms of P and the Jacobian of f. It is shown that: (a) reduction techniques are more accurate when the time rate of change of the response y is relatively small; (b) the change in response between two successive stations contributes to the errors at future stations after the change in response is transformed by a filtering matrix H, defined in terms of P; (c) the error committed at a station propagates to future stations by a mixing and scaling matrix G, defined in terms of P, Jacobian of f, and time increment h. The paper discusses the conditions under which the reduction errors may be minimized and gives guidelines for selecting the reduction basis vector, i.e. the columns of P.

Shape Control of Inflatable Reflectors

In this work studied are the means of maintaining the target design geometry of inflatable membranes that are used for low frequency antenna collectors. Considering the deviations from the target state as the linear combinations of a set of given n normalized undesirable displacement patterns (e.g., Fourier-Zernike functions), the linearized thin shell and membrane theories are used to obtain expressions for the components of the corresponding n number of induced macro strain states. Then the problems associated with the failure in implementing by piezofilm actuators all the components of the geometrically compatible macro strain states are studied. As a result of these studies several recommendations are given.

On the placement of active members in adaptive truss structures for vibration control

The problem of optimal placement of active members which are used for vibration control in adaptive truss structures is investigated. The control scheme is based on the method of eigenvalue assignment as a means of shaping the transient response of the controlled adaptive structures, and the minimization of required control action is considered as the optimization criterion. To this end, a performance index which measures the control strokes of active members is formulated in an efficient way. In order to reduce the computation burden, particularly for the case where the locations of active members have to be selected from a large set of available sites, several heuristic searching schemes are proposed for obtaining the near-optimal locations. The proposed schemes significantly reduce the computational complexity of placing multiple active members to the order of that when a single active member is placed.

A parallel Householder tridiagonalization stratagem using scattered square decomposition

The parallel stratagem in this paper uses scattered square decomposition, introduced by G. Fox, for its data assignment and then exploits parallelism in the solution steps of the sequential Householder tridiagonalization algorithm. One may condense a real symmetric full matrix A of order n into a tridiagonal form by the stratagem in concurrent machines where N(= D2) processors are used. Expressions for efficiency and speedup are given for the evaluation of the stratagem. An alternative stratagem which requires less data transmission but more computations is also discussed. The results shown that the Householder Method of tridiagonalization may be implemented on a concurrent machine efficiently by scattered square decomposition provided that the number of matrix elements contained in each processor is much larger than the number of processors of the concurrent machine, and the ratio of the time to transmit one data item from one processor to any other processor to the time to perform a floating-point arithmetic operation is small enough.

Solution errors in finite element analysis

Abstract The development of the finite element method so far indicates that it is a discretization technique especially suited for positive definite, self-adjoint, elliptic systems, or systems with such components. The application of the method leads to the discretized equations in the form of u = f(u) , where u lists the response of the discretized system at n preselected points called nodes. Instead of explicit expressions, vector function f and its Jacobian f,u are available only numerically for a numerically given u. The solution of u = f(u) is usually a digital computer. Due to finiteness of the computer wordlength, the numerical solution u c is in general different from u. Let u ( x , t) denote the actual response of the system in continuum at points corresponding to those of u. In the literature. u ( x , t)- u is called the discretization errors, u - u c the round-off errors, and the s is. u ( x , t)- u c is called the solution errors. In this paper, a state-of-the-art survey is given on the identification, growth, relative magnitudes, estimation, and control of the components of the solution errors.

On nonlinear finite element analysis in single-, multi- and parallel-processors☆

Numerical solution of nonlinear equilibrium problems of structures by means of Newton-Raphson type iterations is reviewed. Each step of the iteration is shown to correspond to the solution of a linear problem, therefore the feasibility of the finite element method for nonlinear analysis is established. Organization and flow of data for various types of digital computers, such as single-processor/single-level memory, single-processor/two-level-memory, vector-processor/two-level-memory, and parallel-processors, with and without sub-structuring (i.e. partitioning) are given. The effect of the relative costs of computation, memory and data transfer on substructuring is shown. The idea of assigning comparable size substructures to parallel processors is exploited. Under Cholesky type factorization schemes, the efficiency of parallel processing is shown to decrease due to the occasional shared data, just as that due to the shared facilities.

DIRECT FINITE ELEMENT EQUATION SOLVING ALGORITHMS

This paper presents and examines direct solution algorithms for the linear simultaneous equations that arise when finite element models represent an engineering system. It identifies the mathematical processing of four solution methods and assesses their data processing implications using concurrent processing.

Computation of eigenpairs of Ax = γBx for vibrations of spinning deformable bodies☆

Abstract It is shown that, when linear theory is used, the general eigenvalue problem related with the free vibrations of spinning deformable bodies is of the type Ax = γ Bx , where A is Hermitian, and B is real positive definite. Since the order n of the matrices may be large, and A and B are banded or block banded, due to the economics of the numerical solution, one is interested in obtaining only those eigenvalues which fall within the frequency band of interest of the problem. The paper extends the well known method of bisections and iteration of Rn to n dimensional complex spaces, i.e. to Cn, so that it can be applied to the present problem.