Orthotropic Elastic Constants Research Articles

Ultrasonic measurement of orthotropic elastic constants of bovine femoral bone.

Using a pulse transmission ultrasound method, we have determined the elastic properties of bone samples taken from along the length and around the periphery of a bovine femur. Twenty specimens, in the form of 5-mm cubes, were tested. All nine of the orthotropic elastic constants were determined for each specimen. Analysis of our data indicate that there are statistically significant variations from the usual assumption of transverse isotropy.

On the non-linear vibrations of rectangular plates

A solution, based on a one-term mode shape, for the large amplitude vibrations of a rectangular orthotropic plate, simply supported on all edges or clamped on all edges for movable and immovable in-plane conditions, is found by using an averaging technique that helps to satisfy the in-plane boundary conditions. This averaging technique for satisfying the immovable in-plane conditions can be used to resolve many anisotropic and skew plate problems where otherwise, when a stress function is used, the integration of the u and v equations becomes difficult, if not impossible. The results obtained herein are compared with those available in the literature for the isotropic case and excellent agreement is found. Results available for the one-term mode shape solutions of these problems are compared and the non-linear effect is presented as functions of aspect ratio and of the orthotropic elastic constants of the plate. The results are further compared with those based on the Berger method and the detailed comparative studies show that the use of the Berger approximation for large deflection static and dynamic problems and its extension to anisotropic plates, skew plates, etc., can lead to quite inaccurate results.

フィラメント・ワインディング圧力容器の力学的特性

The fiberglass-reinforced composites fabricated by the filament-winding technique developed for convex pressure vessels have advantages especially in high specific strength. However, because of an analytical difficulty encountered with the arbitrary configuration and variation of anisotropic properties of shell structures, it is required to establish the analytical method of mechanical characteristics prior to its optimum design.In the present paper, by taking up a nearly spherical pressure vessel fabricated by the in-plane or planar winding technique, an analytical approach is presented to obtain the distributions of orthotropic elastic constants by use of the lamination theory, and then the stresses and strains in a revolutionary shell by the finite element method. As an example, a 480mm diameter rocket chamber developed for the fourth stage of Lambda rocket is analysed and a good agreement with the experimental values obtained in hydrostatic tests is shown to exist.Next, in view of the practical configuration of rocket motor chamber having junctions with adjacent stages, an analytical method of vessel structures with branching support is presented together with the constraint effects on strains in the vicinity of junction.Lastly, the practical loading cases encountered in test firing on the ground and in flight are compared with those under hydrostatic pressure. These three cases exhibit almost the same strain distributions, suggesting the applicability of hydrostatic proof test in the laboratory to check the mechanical characteristics.

Orthotropic elastic constants of wood

Wood tracheids are essentially tubular structures but wood cross sections are characterized by large numbers of triple points or junctures of wall segments from three adjacent cells. A symmetric triple point is taken as an approximation to the basic unit of wood structure. This element is analysed as a linearly elastic, isotropic body. It is shown that bending effects enhance the deformations arising from simple strains so that the overall response of the element is anisotropic. The resulting stiffnesses are ordered $$E_L \user2{ > }E_R \user2{ > }G_{LR} \sim G_{LT} \user2{ > }E_T \user2{ > }G_{RT} $$ for what are considered to be fairly typical element geometries. It is shown that for all geometries the longitudinal Youngs modulus is proportional to the volume fraction of cell wall material.

Analytical Method of Calculation of Orthotropic Elastic Constants of the FRP Plate

In this paper, the “FRP” plate is considered as continuous body having orthotropic elasticity in the region of infinitesimal deformation, and an analytical method is presented for calculating its orthotropic elastic compliance Sij. The conditions given for the calculation are the structure of the composite system and the elastic constants of the fiber and the resin. A typical example treated mainly in this paper is cloth reinforced plastic. The plate is consisted of two parts, one is the part of yarn having some resin which can be treated as an uni-directionally reinforced plastic rod, and the part of pure resin. The property of resin part is isotropic, but the yarn part has orthotropic property. It is assumed that the orthotropic property of the FRP plate has been caused by this orthotropic character of the yarn parts by the angle between the yarn axis and the direction load. The uniform deformation of all parts in the FRP plate is also assumed.Good agreement between calculated values and observed one for elastic constant has been confirmed by some experiments in which model samples made of single layer FRP plates was used.

Bending of Orthogonally Stiffened Plates

Abstract In this paper the flexure theory for plates of orthotropic material is applied in the case of orthogonally stiffened plates using an experimental method to determine plate stiffnesses in bending and in twisting. Once these stiffnesses, or elastic moduli, have been determined by test they may be used in calculating bending deflections for plates of identical stiffened construction but any given boundary conditions. As an example, calculated deflections of a stiffened circular plate with clamped edge are compared with those which were determined experimentally. It is also demonstrated that the theory can be applied to the case of vibration of a stiffened plate if in addition to the orthotropic elastic constants the weight per unit area of the plate is determined. The various experimental results show considerable promise for use of the proposed combination of theory and experimental method in the analysis of both statically and dynamically loaded plates with attached stiffeners.