A.S. Gendy

Generalized thin-walled beam models for flexural-torsional analysis

Abstract With non-uniform warping being an important mode of deformation, supplementary to the other six modes of stretching, shearing, twisting, and bending, we utilize a fairly comprehensive one-dimensional beam theory for the development of a simple finite element model for the analysis of arbitrary thin-walled beams under general loadings and boundary conditions. The formulation is valid for both open- and closed-type sections, and this is accomplished by using a kinematical description accounting for both flexural and warping torsional effects. To eliminate the shear/warping locking in this C0-element, a generalized mixed variational principle is utilized, in which both displacement and strain fields are approximated separately. In this, the strain parameters are of the interelement-independent type, and are therefore eliminated on the element level by applying the relevant stationarity conditions of the employed ‘modified’ Hellinger-Reissner functional, thus leading to the standard form of stiffness equations for implementation. A rather extensive set of numerical simulations are given to demonstrate the versatility of the models in practical applications involving usage of such components in their stand-alone forms as well as in plate/shell stiffening.

On the finite element analysis of the spatial response of curved beams with arbitrary thin-walled sections

Abstract A three-dimensional, two-field, variational formulation is employed to derive the differential equations governing the stretching, shearing, bending, twisting, as well as warping modes of deformations in a spatially curved beam subjected to general loading and boundary conditions. Correspondingly, a simple two-noded finite element model was developed and utilized in a number of numerical simulations. In particular, attention was given to the significant curvature effects on the results in cases involving unsymmetric cross-section of the thin-walled type, in which any inconsistencies introduced when using the classical notion of two different reference lines, i.e., centroid and shear center, for sectional deformations may lead to large errors.

Generalized yield surface representations in the elasto-plastic three-dimensional analysis of frames

Abstract The yield surface equations for three-dimensional frames subjected to combined actions of an axial force, shear forces, bending moments, warping moment, and a torque are derived based on two different approaches: (i) continuum-based description in terms of stress components and (ii) stress resultants. For the former approach, the well-known von Mises model for the stress components of any material point on the cross-section is utilized. Based on the latter approach, two approximated forms for yield surface equations, semi-quadratic and linear, are suggested as reasonable (upper and lower) bounds for two representative cases; i.e., rectangular and wide flange sections. The one-step, fully implicit method of backward Euler is adopted to facilitate the implementation algorithms for the consistent material tangent stiffness and stress updating. The validity of the proposed equations has been clearly demonstrated by a number of numerical simulations for planar and spatial structures.

STRESS PROJECTION, LAYERWISE-EQUIVALENT, FORMULATION FOR ACCURATE PREDICTIONS OF TRANSVERSE STRESSES IN LAMINATED PLATES AND SHELLS

A two-phase scheme for accurate predictions of interlaminar stresses in laminated plate and shell structures has been addressed in this study. A modified superconvergent patch recovery (MSPR) technique has been utilized to obtain accurate nodal in-plane stresses which are subsequently used with the thickness integration of the three-dimensional equilibrium equations to evaluate the transverse shear and normal stresses. Remarkably, the continuity of the resulting interlaminar stresses is automatically satisfied. Such a two-phase scheme has been applied successfully to a simple smeared layer model (SLM), i.e., a low-order quadrilateral hybrid/mixed element (HMSH5). This simple procedure is found to be completely equivalent to the far more computationally expensive alternative approaches, e.g., sophisticated layerwise approach, for flat geometry. A fairly large number of numerical examples have been solved and the results have shown that the proposed scheme is fairly reliable and computationally cost effective.

NONLINEAR DYNAMICS FOR MIXED SHELLS WITH LARGE ROTATION AND ELASTOPLASTICITY

From a more recent and comprehensive perspective, work on the nonlinear dynamic response of plates and shells calls for detailed studies of several important factors. These include the effect of large spatial rotations on the geometric stiffness and inertia operators, the accurate updating procedures for nodal rotations and associated angular velocities and accelerations, as well as material inelasticity (especially for finite strains). Several of these issues are examined here in conjunction with a recently developed mixed finite element formulation for plates and shells. To this end, and restricting the scope to the case of large overall motions but small strains, low-order displacement/strain interpolations are utilized, together with a radial return algorithm (backward-Euler-integration scheme) for plasticity effects. The Newmark implicit scheme has been employed to integrate the semi-discrete equations of motion. A selective set of elastic as well as elasto-plastic problems has been solved to demonstrate the effectiveness and practical utility of the formulation described for plate and shells with arbitrary geometry.

MIXED FINITE ELEMENT MODELING FOR THE DYNAMICS OF BEAM ASSEMBLAGES UNDERGOING LARGE OVERALL MOTIONS IN SPACE

The fully nonlinear dynamic analysis of space frames constitutes a very challenging class of finite element applications. To date, experiences with such solutions have been limited mostly to the conventional displacement-based approaches, and it is the main objective here to report on the use of the alternative mixed scheme in such general dynamical treatments; i.e., for beam assemblages undergoing large overall motions in space and subjected to both conservative and non-conservative forces. In this, such factors as (i) effect of large spatial rotations on the geometric stiffness and inertia operators; (ii) the need for the accurate updating procedures for nodal rotations, and associated angular velocities/accelerations; (iii) material in-elasticity; and (iv) load correction matrices for configuration-dependent conservative and non-conservative forces/moments become important. To this end, and restricting the scope to the case of large overall motions but small strains, we utilize the simplest of low-order displacement/strain interpolations, for the hybrid-mixed form, together with a radial return algorithm (backward-Euler-intergration scheme) for plasticity effects. The semi-discrete equations of motion have been integrated with the Newmark implicit scheme. A comprehensive set of elastic as well as elasto-plastic problems, under both conservative and non-conservative loading, has been solved to demonstrate the effectiveness and practical utility of the formulation described.

Design optimization of a spacer structure for Space Station Freedom

Abstract Structure optimization techniques, which have matured over the last three decades, have been applied successfully to generate a preliminary minimum weight design of a Space Station Freedom component. The design code ‘COMETBOARDS’ which was developed by the Structural Mechanics Branch of NASA Lewis Research Center, was utilized. The component, termed a ‘short spacer truss’ of the Space Station Freedom, was modeled as a space frame, and its minimum-weight design was obtained under prescribed stress, buckling, crippling, displacement, and frequency constraints. The optimum design weight was found to be lighter than that obtained manually. The optimum design also appears to be attractive from manufacturing considerations. A description of the structural component, its design environment, behavior limitations, and the optimum-design process are briefly presented in this paper, along with a brief description of the design code COMETBOARDS that was developed for this purpose.

Weight minimization of flight components

Abstract Minimizing the weight of structural components of the Space Station launched onto orbit in a space shuttle can save cost, reduce the number of space shuttle missions and facilitate on-orbit fabrication. Traditional manual design of such components, although feasible, cannot represent a minimum weight condition. At NASA Lewis Research Center, a design capability called CometBoards (which is an acronym for comparative evaluation test bed of optimization and analysis routines for the design of structures) has been developed especially for the design optimization of such flight components of the Space Station—a spacer structure and a support system—illustrating the capability of CometBoards. These components are designed for loads and behavior constraints that arise from a variety of flight accelerations and maneuvers. The optimization process using CometBoards reduced the weights of the components by one third from those obtained with traditional manual design. This paper presents a brief overview of the design code CometBoards; and a description of the Space Station components, their design environments, behavior limitations and attributes of their optimum designs.