Suha Oral

Optimum design of composite structures with curved fiber courses

Abstract In this study, a new methodology for the optimum design of laminated composites with curved fiber courses is presented. The objective of the optimization problem is to minimize the weight of the composite laminate under stress constraints. The Tsai–Hill criterion is employed on the first ply failure basis. Layer thicknesses and fiber angles are represented by bicubic Bezier surfaces and cubic Bezier curves, respectively. Design variables are coordinates of control points of the corresponding Bezier splines. The design variable linking procedure is used in order to reduce the number of design variables further and to provide symmetry in the design. The sequential quadratic programming is used in the optimization. The modeling of the laminate is carried out by using three-node shell finite elements.

Optimum design of high-speed flexible robotic arms with dynamic behavior constraints

Abstract A methodology is presented for the optimum design of robotic arms under time-dependent stress and displacement constraints by using mathematical programming. Finite elements are used in the modeling of the flexible links. The design variables are the cross-sectional dimensions of the elements. The time dependence of the constraints is removed through the use of equivalent constraints based on the most critical constraints. It is shown that this approach yields a better design than using equivalent constraints obtained by the Kresselmeier-Steinhauser function. An optimizer based on sequential quadratic programming is used and the design sensitivities are evaluated by overall finite differences. The dynamical equations contain the nonlinear interactions between the rigid and elastic degrees-of-freedom. To illustrate the procedure, a planar robotic arm is optimized for a particular deployment motion by using different equivalent constraints.

A shear-flexible facet shell element for large deflection and instability analysis

Abstract A facet shell element based on an anisoparametric plate bending element and a quadratic plane-stress element with vertex rotations is formulated for geometrically nonlinear analysis of shells. The updated Lagrangian formulation which proves to be effective for three-node elements is employed. The restriction of small rotation between the increments is removed by using Hsiaos finite rotation method in which the rigid body motion is eliminated from the total displacement. The displacement control is used to alleviate the singularity of the tangential stiffness matrix in the limit point type problems. Numerical solutions are presented for beams, plates and shells to evaluate the performance of the element.

A shear flexible finite element for nonuniform, laminated composite beams

Abstract A shear flexible finite element is formulated for linearly tapered, symmetrically laminated composite beams. The element has three nodes and 18 degrees of freedom. The three-node configuration is obtained from a five-node parent element by constraining the shear angle variation to be linear. The bending in two planes, twisting and stretching are considered. The performance of the element is tested with isotropic and composite materials, constant and variable cross-sections, and straight and curved geometries. The element proves to be accurate and versatile. The compatibility with plate and shell elements as a stiffener is assured through the use of simple nodal variables of C0-type.

A Mindlin plate finite element with semi-analytical shape design sensitivities

Abstract A hybrid-stress Mindlin plate finite element and its sensitivity derivatives are presented. The element is triangular and has a simple nodal configuration with three corner nodes and C o type nodal variables. The use of independent field assumptions for displacements and stresses removes the necessity for an in-plane shear correction factor. The element can effectively be used as the bending part of facet shell elements. Its simplicity and accuracy makes it ideal for large-scale analysis and design problems. The sensitivity derivatives are obtained by analytical and semi-analytical methods for the thickness and shape design variables, respectively. The well-known deficiency of the classical semi-analytical method in the shape design of flexural systems is alleviated by using a series approximation for the sensitivity derivatives and considering the higher order terms. The accuracy of the proposed formulations in computing displacements, stresses and sensitivity derivatives is verified by numerical examples.

An improved semianalytical method for sensitivity analysis

The semi-analytical method is conveniently used to obtain design sensitivities. However, it may have serious accuracy problems in shape design. In this study, an improved semianalytical method is presented for the accurate computation of shape design sensitivities. The method is based on approximating the flexibility matrix by means of von Neumann series. In numerical examples, two cases for which the standard semianalytical method fails are considered. It is demonstrated that the sensitivities can be obtained very accurately by the improved method proposed.

The optimum die profile for the cylindrical bending of plates

Abstract This paper presents a methodology for the design of plate-forming dies in cylindrical bending using optimization techniques to reduce the cost of die production by reducing the trial-and-error procedure considerably in determining the final die geometry. The plate thickness is discretized by plane-strain finite-elements. The die is taken to be rigid and its profile is approximated by Bezier curves the control-point coordinates of which are the design variables. The die profile is varied to minimize the difference between the required shape and the shape of the bent plate, considering springback action. The unconstrained optimization problem is solved by the BFGS (Broyden-Fletcher-Goldfarb-Shanno) method. A numerical example is presented where the optimum die profile is obtained for a plate bent into a quarter circle.

A Three-Node Shear-Flexible Hybrid-Stress Finite Element for the Analysis of Laminated Composite Plates

A cost-effective, shear-flexible hybrid-stress element is developed for lami nated composite plates based on the Yang-Norris-Stavsky theory. The element is triangular and has vertex nodes only. The nodal variables are three displacements and two indepen dent normal rotations of C° type. The assumed stress field is linear. The assumed displace ment field is based on the anisoparametric interpolations in which the rotations and in- plane displacements are linear and the transverse displacement is quadratic. The element is invariant and non-locking. The results of the numerical studies show that the present el ement converges rapidly and monotonically in all thickness regimes.

A hybrid-stress finite element for nonuniform filament-wound composite box-beams

A two-node, hybrid-stress finite element is formulated for static and dynamic analyses of linearly tapered, filament-wound composite box-beams. The effects of shear deformation and rotatory inertia are taken into account. The extensional, flexural and torsional actions are modeled. The element is assessed by a number of static and dynamic test problems for uniform and nonuniform, isotopic and composite box-beams. The results show the accuracy of the formulation.

A pseudo-layered, elastic-plastic, flat-shell finite element

Abstract A three-node, C0-type, layered flat-shell finite element is developed for the analysis of large elastic-plastic deformations in plate and shell structures. The system equations are derived by using virtual work principle and the updated Lagrangian formulation. Material is assumed to be isotropic and rate insensitive obeying J2-flow rule. The displacement field assumption of the MIN3 plate bending element is employed. A layered structure is used to model through-the-thickness distribution of elastic and plastic zones. The finite element results for three nonlinear plate bending problems are compared with experimental results to verify the accuracy of the formulation.