Showing papers by "Jack R. Vinson published in 1993"

Curvilinear Coordinate Systems

Abstract: Shells involve thin walled elastic bodies wherein one dimension is considerably smaller than the other two, but in which the midsurface is curved in at least one direction. Thus, to describe a shell succinctly, curvilinear coordinates must be employed. This causes considerable complications in the mathematical descriptions and operations, not existing in the same equations posed in a Cartesian coordinate system. It would be proper to introduce the subject of shell theory by preceding it with a course in topology. However, in what follows, the description of mathematics involving curvilinear coordinates is given, sufficient only to derive the general shell equations. In no way is the presentation rigorous or inclusive. Other texts such as Malvern (Reference 1.1) and Sokolnikoff [1.2] should be consulted by those who wish to learn more.

Cylindrical Shells of Composite Materials

Abstract: In considering cylindrical shells of composite anisotropic materials the equilibrium equations, strain-displacement equations and compatibility equations are the same as those used in Chapter 3 for cylindrical shells of isotropic materials. Only the stress-strain relations (i.e. the constitutive relations) differ. For the most general case the proper constitutive relations are given by (14.63) and (14.61).

Derivation of the Governing Equations for Thin Shells

Abstract: After the brief introduction to curvilinear coordinates in Chapter 1, one can now describe the equations of elasticity in curvilinear coordinates, and systematically reduce them to the governing equations for shells in curvilinear coordinates, employing the assumptions of shells in the process.

Very Thick Walled Composite Shells

Abstract: In Chapter 13, methods of analysis are presented for very thick walled isotropic cylindrical bodies of h/R≤05 which were developed by Vinson [136, 137] More recently, Waltz [231] extended those methods to the much more complicated case of a cylindrical shell body with h/R≤05 composed of a specially orthotropic composite material While of much interest and use, the approach, method, assumptions, etc of this research exactly parallels that of the isotropic thick walled shell methods, and therefore is hereby referred to but not included specifically, because of its length and complexity However, Reference [231] is complete and ready for use by engineers for design and analysis of very thick walled specially orthotropic composite material shells

Energy Methods for Shells

Abstract: In structural mechanics three energy principles are used Minimum Potential Energy, Minimum Complementary Energy, and Reissner’s Variational Theorem. The first two are discussed at length in Sokolnikoff [10.1] and many other references. The Reissner Variational Theorem, likewise, is widely referenced. In solid mechanics, Minimum Complementary Energy is rarely used, because often it requires assuming continuous functions for all stresses which satisfy the boundary conditions, are continuous and satisfy equilibrium. It is usually far easier to make a guess at the displacement functions which must be continuous and satisfy the boundary conditions. These displacement functions are needed to utilize the Theorem of Minimum Potential Energy.

Shells of Sandwich Construction

Abstract: Sandwich construction, like the name implies, usually consists of two faces which are kept separated by a core. The facings usually carry the in-plane primary loads (tensile, compressive, and in-plane shear), while the core (analogous to the web of an I-beam) resists the transverse shear loads. The two faces usually are composed of the same material, and have the same thickness (tf), which places the neutral surface of bending at the mid-plane of the sandwich cross-section, as shown in Figure 24.1 (a).

Energy Methods in Composite Material Shells

Abstract: Many composite material structures not only involve anisotropy, multilayer considerations and transverse shear deformat mal effects, which can be very important. True, for preliminary design and analysis one often uses the simplified, easier to use analyses that have been presented earlier, but for the final design, transverse shear deformation and hygrothermal effects must be included. These thermal and moisture effects have been described in Chapter 14. Analytically they cause considerable difficulty, because with their inclusion few boundary conditions are homogeneous, hence separation of variables, used throughout the shell solutions to this point, cannot be utilized straightforwardly. Only through the laborious process of transformation of variables can separation of variables be used [See 22.1, pp. 63–66]. Therefore, energy principles are much more convenient for use in design and analyses of plate and shell structures when hygrothermal effects are present. Recently, the incorporation of piezoelectric effects, analogous to the thermal and hygrothermal effects, provides another source of nonhomogenous boundary conditions [22.2].

Paraboloidal Shells of Revolution

Abstract: De Silva [17.28] has considered the problem of axisymmetric loading of thin elastic paraboloidal shells of revolution which includes the effect of transverse shear deformation by using equations developed by Naghdi [19.1]. The transverse shear deformation is accounted for due to thickness considerations, and the material system considered is isotropic. That differs from the present theory which accounts for transverse shear deformation because of the large Eo/Goξ and Eθ/Gθξ ratios involved with many composite materials although the shell is geometrically thin. Therefore, the two theories are not identical.

Vibration of Isotropic Shells

Abstract: Entire texts are needed to discuss shell vibrations in their entirety. In this Chapter, axially symmetric vibrations are discussed first so that through their simplicity, it is easy to see how static equations are easily transformed to dynamic equations, and to show the relation to the vibrations of beams: with and without an elastic foundation. Next, the general vibration characteristic of shells are shown through the study of cylindrical shells, also relating the behavior to beam vibrations. Through the work of Koga, only five types of boundary conditions are needed to study any and all boundary conditions. Next, the time portion of dynamic loads is presented in an easy to use manner to study impact response of shells. Finally, the important areas of shells vibrating in beam modes is studied, using two different approaches. This chapter and the references given provide a background for further study of shell vibrations. In Chapter 21, the vibrations of composite shells is discussed and could be studied upon completing this Chapter.

Thermoelastic Effects on Shells

Abstract: In the entire text to this point, attention has been focused on the isothermal elastic behavior of classical shells. The effect that temperature distributions within the shell may have on stresses, strains and displacements has not been discussed.

Shells of Revolution Subjected to Axially Symmetric Loads

Abstract: Shells in which the middle surface is generated by rotating a generator about an axis are called shells of revolution. A closed cylindrical shell is the simplest case, and the analysis of stresses and deformations in such cylindrical shells was treated in Chapter 3. Due to Reissner, Meissner, and Naghdi, a generalized method of analysis can be employed for all shells of revolution subjected to axially symmetric loads without dealing with each shell geometry specifically. This treatment is presented below, because of its extreme usefulness.

Laminated Shells and Adhesive Bonded Joints

Abstract: Laminated construction has many structural applications. However, in all such construction, structural reliability is predicated on the fact that the laminae remain joined together, otherwise many of the advantages of employing dissimilar materials together are lost. Questions then arise as to whether thin bonds, thick bonds, pliable bonds or stiff bonds should be used between laminae. Certainly it is very important to know the state of stresses throughout the bond to determine the bond material requirements. A detailed discussion of bonded joints and laminated construction could be a volume in itself. In this section, the simplest case of a laminated cylindrical isotropic shell is discussed in order to present all of the important considerations with a minimum of complexity. More complicated problems will be discussed in Part II of this text.

Orthotropic Shells of Revolution Including Transverse Shear Deformation and Thermal Thickening

Abstract: Just as in Chapter 4, which dealt with shells of revolution composed of isotropic materials, the same general approach can be used for shells of revolution composed of composite materials, following Daugherty [17.1].

Buckling of Composite Material Shells

Abstract: Analogous to Chapter 11, treating the buckling of shells of isotropic materials, this Chapter presents analogous results for the buckling of shells which involve anisotropic, layered composite construction. Cylindrical shells are treated herein, unless otherwise specifically noted. All of the equations presented herein emanate from Reference 20.1.

Ellipsoidal and Spherical Composite Shells

Abstract: In this Chapter, the methods and equations developed in Chapter 17 for orthotropic thin shells of revolution including transverse shear deformation, thermal loadings, and thermal thickening will be applied to ellipsoidal shells of revolution. This will be accomplished by considering the homogeneous and particular solutions separately.

Very Thick Walled Cylindrical Shells

Abstract: As performance requirements increase for pressure vessels and deep submergence vehicles, as the need increases for higher pressure test facilities, and because arteries and veins have the geometry they do, there is an increased need for a shell theory for very thick shells; say, a wall thickness to mean shell radius ratio (h/R) of 0.5. Such a theory is presented here. In addition, explicit solutions are provided in order to analyze a finite length circular cylindrical shell under both axially symmetric lateral distributed loading and in-plane loads, composed of an isotropic material.

Composite Conical Shells

Abstract: Conical shells of isotropic materials were treated in Chapter 5 earlier. In that chapter the classical theory was used, and no thermoelastic considerations were included.

Vibrations of Shells Composed of Composite Materials

Abstract: This Chapter is in no way a comprehensive portrayal of the voluminous literature on the vibration of composite shells. Subsequent to studying the vibrations of isotropic shells in Chapter 12, the intent here is to provide some insight into the vibration behavior, some techniques available for solution, and some awareness of the peculiarities associated with composite shells.

Shells Of Other Shapes

Abstract: In the preceding chapters, cylindrical shells, general shells of revolutions, conical shells and spherical shells have been treated, and some solutions were obtained In this chapter the governing equations and geometric relations for some other shell shapes are provided, with no solutions, as an aid to solving problems, and giving insight as to how to approach these other problems