Maximum Torsional Stiffness Research Articles

Numerical/Experimental Validation of Thin-Walled Composite Box Beam Optimal Design

Thin-walled composite box beam structural configuration is representative of a specific high aspect ratio wing structure. The optimal design procedure and lay-up definition including appropriate coupling necessary for aerospace applications has been identified by means of “ad hoc” analytical formulation and by application of commercial code. The overall equivalent bending, torsional and coupled stiffness are derived and the accuracy of the simplified beam model is demonstrated by the application of Altair Optistruct. A simple case of a coupled cantilevered beam with load at one end is introduced to demonstrate that stiffness and torsion angle distribution does not always correspond to the trends that one would intuitively expect. The maximum of torsional stiffness is not obtained with fibers arranged at 45° and, at the maximum torsional stiffness, there is no minimum rotation angle. This observation becomes essential in any design process of composite structures where the constraints impose structural couplings. Furthermore, the presented theory is also extended to cases in which it is necessary to include composite/stiffened hybrid configurations. Good agreement has been found between the theoretical simplified beam model and numerical analysis. Finally, the selected composite configuration was compared to an experimental test case. The numerical and experimental validation is presented and discussed. A good correlation was found confirming the validity of the overall optimization for the optimal lay-up selection and structural configuration.

Optimization of Torsional Stiffness for Heavy Commercial Vehicle Chassis Frame

The chassis frame is the backbone of a heavy commercial vehicle (HCV). Its main purpose is to securely carry the determined load under all designed operative situations. Thus, it should be rigid enough to withstand the various forces acting on it. The objective of this study was to develop a stiffness model to select an optimum cross section with determined torsional stiffness. Johnson's method of optimization was adapted to develop a stiffness equation and select a section with a determined torsional stiffness and a required mass constraint. The stiffness obtained from the developed stiffness model and finite element analysis (FEA) is a close match, which proves the validity of the proposed model. The section with the maximum torsional stiffness was used for frame-level optimization to improve the torsional and lateral stiffness of the overall chassis frame. The strain energy absorption capacity of the cross member improved by changing the section of the cross member. By using the optimized section, the torsional stiffness of the frame improved by 44% and a lateral stiffness of 10% was obtained. The Creo software was used for modeling and FEA was performed with the Hypermesh software.

복합재 코일스프링 개발을 위한 수치해석 및 실험적 연구

This paper shows the feasibility of using carbon-fiber-reinforced polymer (CFRP) composite materials for manufacturing automotive coil springs. For achieving weight reduction by replacing steel with composite materials, it is essential to optimize the material parameters and design variables of the coil spring. First, the shear modulus of a CFRP beam model, which has 45° ply angles for maximum torsional stiffness, was calculated and compared with the test results. The diameter of the composite spring was predicted to be 17.5 mm for ensuring a spring rate equal to that when using steel material. Finally, a finite element model of the composite coil spring with 45° ply angles and 17.5 mm wire diameter was constructed and analyzed for obtaining the static spring rate, which was then compared with experimental results.

On a method of solving a shape optimization problem in elasticity theory

The problem of calculation of the shape of a doubly-connected transverse section of an elastic homogeneous prismatic rod possessing maximum torsional stiffness is considered. The shape of its internal prismatic cavity is here assumed to be fixed while the area of the rod transverse cross-section is constant.

Optimization of a Thin-Walled, Anisotropic Curved Bar for Maximum Torsional Stiffness∗

ABSTRACT ABSTRACT A curved bar in the form of a circular ring sector is under uniform torsion when acted upon by two equal and opposite forces directed alone the axis passing through the center of the ring and perpendicular to its plane, i.e., forces acting along the axis of rotation. The exact torsion theory can be extended to this case when the material of which the bar consists is cylindri-cally anisotropic, with the axis of anisotropy directed along the axis of rotation and having an elastic symmetry about any plane of the transverse cross section. In this paper, a thin-walled curved bar having the loading conditions and material properties described above is optimized so as to maximize its torsional stiffness. The optimization is carried out with respect to the cross-sectional shape of the bar subject to constraints on the transverse area (single-purpose design) and bending stiffness (multipurpose design). In the special case of an orthotropic material, the angle of inclination of the ortho-tropy axe...

Optimality conditions in the problem of seeking the hole shapes in elastic bodies: PMM vol. 41, n≗ 5, 1977, pp. 920–925

Seeking the optimal hole shapes in elastic bodies, which cause minimal stress concentration, results in minimax optimization problems with a local criterion. These problems are considered in this paper within the framework of plane elasticity theory, and it is proved that holes with equi-stressed boundaries are optimal. Problems of boundary optimization were investigated earlier in[1–4] in connection with seeking the shapes of twisted rods possessing maximum torsional stiffness, and problems to construct equi-stressed holes in plates were studied in [5–8].

Determination of the shapes of doubly-connected bar sections of maximum torsional stiffness: PMM vol. 40, n≗ 6, 1976, pp. 1078–1084

The problem of determining the shape of the transverse section of a prismatic bar with a prismatic longitudinal cavity (hole) of given shape, subjected to torsion, from the condition that the torsional stiffness would be maximal for a given cross-sectional area, is considered. The apparatus of complex variable function theory is used to determine the outline required. Examples of computing the outlines of the sections for elliptical, square, and rectangular hole shapes are presented.

A Movable-Mass Attitude Stabilization System For Cable-Connected Artificial-^ Space Stations

The development of an active, momentum-exchange system to be used for attitude stabilization of a class of cable-connected artificial-g space stations is studied. A system which employs a single movable control mass is examined for the control of a space station which has the physical appearance of two cylinders connected axially by cables. The dynamic model for the space station includes its aggregate rigid body rotation and relative torsional rotation between the bodies. A zero torsional stiffness design (one cable) and a maximum torsional stiffness design (eight cables) are examined in various stages of deployment, for selected spin velocities ranging from 4 rpm upwards. A linear, time-invariant, feed-back control system is employed, with gains calculated via a root-specification procedure. The movable mass controller provides critical wobble-damping capability for the crew quarters for all configurations and spin velocity.

Tubes of Optimum Bending Stiffness: An Analogy

The torsional stiffness of a thin-walled tube of given perimeter and thickness varies as the square of the enclosed area. The shape giving maximum torsional stiffness is therefore a circle, this being the curve with maximum area for given perimeter. We consider here the nature of the corresponding curve for maximum bending stiffness. The quantity to be made a maximum is now, not the area within the curve, but the second moment for the whole curve about the bending axis. This will give the greatest “moment of inertia” for a tube of uniform thickness. The theory is given in the Appendix and typical forms are shown in Fig. 3. A finite length of base has to be assumed; otherwise the curve reduces to a single straight line normal to the axis.