The Experts below are selected from a list of 234 Experts worldwide ranked by ideXlab platform
Eric M. Austin - One of the best experts on this subject based on the ideXlab platform.
-
Local Effects of Piezopolymer Patches on Inflatable Space-Based Structures
Journal of Spacecraft and Rockets, 2002Co-Authors: Robert Brett Williams, Eric M. Austin, Daniel J. InmanAbstract:Inflatable structures are often characterized as Membranes (that is, structural elements that cannot resist bending moments). This simplification raises the question of whether Membrane Theory can account for the effects of active, surface-mounted piezopolymer patches. This work discusses these effects on the dynamic behavior of a flat, rectangular coupon section and assesses the patch's ability to sense and actuate transverse deflections of the thin-film substrate using traditional Membrane Theory. The Rayleigh-Ritz method was employed to approximate the natural frequencies and mode shapes of this layered system. Although including the additional mass of the patch, traditional Membrane Theory was unable to account for the added stiffness of the patch layer. When the piezoelectric behavior of the patch was considered, Membrane Theory failed to model the piezopolymer as a useful sensor. Also, excitation of transverse vibrations was not possible using Membrane Theory, which does not allow application of bending moments. However, piezoelectric actuation was modeled as applied in-plane forces, which enabled the patch to suppress out-of-plane disturbances by altering the tension in the base layer as a function of applied voltage.
-
Limitations of Using Membrane Theory for Modeling PVDF Patches on Inflatable Structures
Journal of Intelligent Material Systems and Structures, 2001Co-Authors: Robert Brett Williams, Daniel J. Inman, Eric M. AustinAbstract:An underlying goal in structural modeling is to use the simplest mathematics possible that captures the physics of a problem accurately. Inflatable structures are normally fabricated from thin films, so they are often modeled as Membranes, i.e., structural elements that cannot resist bending moments. Researchers have recently been looking at active control of inflated structures, so this raises the question of whether Membrane Theory can account for the effects of surface-mounted piezopolymer patches used as either sensors or actuators. This work discusses these effects on the dynamic behavior of a flat, rectangular coupon section and assesses the patch's ability to sense and actuate transverse deflections of the thin film substrate using traditional Membrane Theory. The Rayleigh-Ritz method was employed to approximate the natural frequencies and mode shapes of this layered system. While including the additional mass of the patch, traditional Membrane Theory was unable to account for the added stiffness of the patch layer. When the piezoelectric behavior of the patch was considered, Membrane Theory failed to model the PVDF as a useful sensor. Also, excitation of transverse vibrations was not possible using Membrane Theory, which does not allow application of bending moments. However, PVDF actuation was modeled as an applied in-plane force, which allowed the patch the ability to suppress out-of-plane disturbances by altering the tension in the base layer as a function of applied voltage, This article discusses the limitations associated with using traditional Membrane Theory to analyze the dynamic behavior of thin-layered systems as well as model the interaction between an active PVDF patch and the torus substrate.
Johan Blaauwendraad - One of the best experts on this subject based on the ideXlab platform.
-
Membrane Theory for Shells with Principal Curvatures
Structural Shell Analysis, 2013Co-Authors: Johan Blaauwendraad, Jeroen H. HoefakkerAbstract:The basic assumption of Membrane Theory is that a thin shell produces a pure Membrane stress field, and that no bending stresses occur. This assumption is applicable if certain boundary and loading conditions, exemplified in Chap. 1, are met. In this pure Membrane stress field, only normal and in-plane shear stresses are produced. They are due to stretching and shearing of the middle plane of the shell. Bending, torsion and transverse shear stresses are not accounted for.
-
Membrane Theory for Thin Shells of Arbitrary Curvatures
Structural Shell Analysis, 2013Co-Authors: Johan Blaauwendraad, Jeroen H. HoefakkerAbstract:The three sets of equations of Chap. 2 derived for the Membrane behaviour of thin shells relate to a co-ordinate system placed according to the principal curvatures. In practice it may be useful to choose the co-ordinate system in such a way that a co-ordinate axis is placed along an edge of the shell, which does not necessarily coincide with a principal curvature. This is the subject of this chapter. Different from the approach of Chap. 2, we now choose a reference system of axes in the tangent plane of a point O at the middle surface of the shell. The x-axis and y-axis are in the tangent plane, and the z-axis is normal to the plane. Instead of the principal curvatures k 1 and k 2, we now work with curvatures k x and k y . On top of that, it will appear to be convenient to define a twist k xy . The expressions for the curvatures k x and k y are in fact the same as in Chap. 2, but we will derive them again in an alternate way, such that it is easy to extrapolate to the derivation of the twist k xy .
-
Application of Membrane Theory to Circular Cylindrical Shells
Structural Shell Analysis, 2013Co-Authors: Johan Blaauwendraad, Jeroen H. HoefakkerAbstract:For a circular cylindrical shell, it is convenient to apply a polar co-ordinate system to the cross-sectional profile as illustrated in Fig. 4.1. The axes are chosen in the longitudinal, circumferential and transverse directions.
-
Plate Membrane Theory
Plates and FEM, 2009Co-Authors: Johan BlaauwendraadAbstract:The word plate is a collective term for systems in which transfer of forces occurs in two directions; walls, deep beams, floors and bridge slabs are all plates. We distinguish two main categories, plates that are loaded in their plane, and plates loaded perpendicularly to their plane. For both categories we give an approach with differential equations, such that a basic understanding is provided and for certain characteristic cases an exact solution can be determined. We follow the displacement method, working with differential equations. In plates that are loaded in their plane, the plane stress state is called the Membrane state. All stress components are parallel to the mid- plane of the plate. In special cases we can simply determine the stresses.
-
Applications of the Plate Membrane Theory
Plates and FEM, 2009Co-Authors: Johan BlaauwendraadAbstract:In this chapter we will give solutions for plates, which are loaded only on their edges. This implies that no distributed forces px and py occur, and the fourth-order bi-harmonic equation (1.23) reduces to the simple form $$\nabla^2\nabla^2 u_x=0$$ (2.1) When a general solution has been found for u x , the solution for u y can be derived from the relation between u x and u y as given in Eq. (1.17). If we choose the first equation, the relation is (P x = P y = 0) $$\left(\frac{\partial^2}{\partial x^2}+\frac{1-\nu}{2}\frac{\partial^2}{\partial y^2}\right)u_x+\left(\frac{1+\nu}{2}\frac{\partial^2}{\partial x\partial y}\right)u_y=0$$ (2.2) We will demonstrate two types of solution. In the first type, solutions for the displacements u x and u y will be tried, which are polynomials in x and y. We will see that interesting problems can be solved through this ’inverse method‘. The second type of solution is found by assuming a periodic distribution (sine or cosine) in one direction. Then in the other direction an ordinary differential equation has to be solved. This approach is suitable for deep beams or walls.
Robert Brett Williams - One of the best experts on this subject based on the ideXlab platform.
-
Local Effects of Piezopolymer Patches on Inflatable Space-Based Structures
Journal of Spacecraft and Rockets, 2002Co-Authors: Robert Brett Williams, Eric M. Austin, Daniel J. InmanAbstract:Inflatable structures are often characterized as Membranes (that is, structural elements that cannot resist bending moments). This simplification raises the question of whether Membrane Theory can account for the effects of active, surface-mounted piezopolymer patches. This work discusses these effects on the dynamic behavior of a flat, rectangular coupon section and assesses the patch's ability to sense and actuate transverse deflections of the thin-film substrate using traditional Membrane Theory. The Rayleigh-Ritz method was employed to approximate the natural frequencies and mode shapes of this layered system. Although including the additional mass of the patch, traditional Membrane Theory was unable to account for the added stiffness of the patch layer. When the piezoelectric behavior of the patch was considered, Membrane Theory failed to model the piezopolymer as a useful sensor. Also, excitation of transverse vibrations was not possible using Membrane Theory, which does not allow application of bending moments. However, piezoelectric actuation was modeled as applied in-plane forces, which enabled the patch to suppress out-of-plane disturbances by altering the tension in the base layer as a function of applied voltage.
-
Limitations of Using Membrane Theory for Modeling PVDF Patches on Inflatable Structures
Journal of Intelligent Material Systems and Structures, 2001Co-Authors: Robert Brett Williams, Daniel J. Inman, Eric M. AustinAbstract:An underlying goal in structural modeling is to use the simplest mathematics possible that captures the physics of a problem accurately. Inflatable structures are normally fabricated from thin films, so they are often modeled as Membranes, i.e., structural elements that cannot resist bending moments. Researchers have recently been looking at active control of inflated structures, so this raises the question of whether Membrane Theory can account for the effects of surface-mounted piezopolymer patches used as either sensors or actuators. This work discusses these effects on the dynamic behavior of a flat, rectangular coupon section and assesses the patch's ability to sense and actuate transverse deflections of the thin film substrate using traditional Membrane Theory. The Rayleigh-Ritz method was employed to approximate the natural frequencies and mode shapes of this layered system. While including the additional mass of the patch, traditional Membrane Theory was unable to account for the added stiffness of the patch layer. When the piezoelectric behavior of the patch was considered, Membrane Theory failed to model the PVDF as a useful sensor. Also, excitation of transverse vibrations was not possible using Membrane Theory, which does not allow application of bending moments. However, PVDF actuation was modeled as an applied in-plane force, which allowed the patch the ability to suppress out-of-plane disturbances by altering the tension in the base layer as a function of applied voltage, This article discusses the limitations associated with using traditional Membrane Theory to analyze the dynamic behavior of thin-layered systems as well as model the interaction between an active PVDF patch and the torus substrate.
Daniel J. Inman - One of the best experts on this subject based on the ideXlab platform.
-
Local Effects of Piezopolymer Patches on Inflatable Space-Based Structures
Journal of Spacecraft and Rockets, 2002Co-Authors: Robert Brett Williams, Eric M. Austin, Daniel J. InmanAbstract:Inflatable structures are often characterized as Membranes (that is, structural elements that cannot resist bending moments). This simplification raises the question of whether Membrane Theory can account for the effects of active, surface-mounted piezopolymer patches. This work discusses these effects on the dynamic behavior of a flat, rectangular coupon section and assesses the patch's ability to sense and actuate transverse deflections of the thin-film substrate using traditional Membrane Theory. The Rayleigh-Ritz method was employed to approximate the natural frequencies and mode shapes of this layered system. Although including the additional mass of the patch, traditional Membrane Theory was unable to account for the added stiffness of the patch layer. When the piezoelectric behavior of the patch was considered, Membrane Theory failed to model the piezopolymer as a useful sensor. Also, excitation of transverse vibrations was not possible using Membrane Theory, which does not allow application of bending moments. However, piezoelectric actuation was modeled as applied in-plane forces, which enabled the patch to suppress out-of-plane disturbances by altering the tension in the base layer as a function of applied voltage.
-
Limitations of Using Membrane Theory for Modeling PVDF Patches on Inflatable Structures
Journal of Intelligent Material Systems and Structures, 2001Co-Authors: Robert Brett Williams, Daniel J. Inman, Eric M. AustinAbstract:An underlying goal in structural modeling is to use the simplest mathematics possible that captures the physics of a problem accurately. Inflatable structures are normally fabricated from thin films, so they are often modeled as Membranes, i.e., structural elements that cannot resist bending moments. Researchers have recently been looking at active control of inflated structures, so this raises the question of whether Membrane Theory can account for the effects of surface-mounted piezopolymer patches used as either sensors or actuators. This work discusses these effects on the dynamic behavior of a flat, rectangular coupon section and assesses the patch's ability to sense and actuate transverse deflections of the thin film substrate using traditional Membrane Theory. The Rayleigh-Ritz method was employed to approximate the natural frequencies and mode shapes of this layered system. While including the additional mass of the patch, traditional Membrane Theory was unable to account for the added stiffness of the patch layer. When the piezoelectric behavior of the patch was considered, Membrane Theory failed to model the PVDF as a useful sensor. Also, excitation of transverse vibrations was not possible using Membrane Theory, which does not allow application of bending moments. However, PVDF actuation was modeled as an applied in-plane force, which allowed the patch the ability to suppress out-of-plane disturbances by altering the tension in the base layer as a function of applied voltage, This article discusses the limitations associated with using traditional Membrane Theory to analyze the dynamic behavior of thin-layered systems as well as model the interaction between an active PVDF patch and the torus substrate.
R L Taylor - One of the best experts on this subject based on the ideXlab platform.
-
Theory and finite element formulation of rubberlike Membrane shells using principal stretches
International Journal for Numerical Methods in Engineering, 1992Co-Authors: Friedrich Gruttmann, R L TaylorAbstract:A Theory of rubberlike Membrane shells undergoing large elastic deformations is derived. The stresses are deduced from Ogden's material law, which is formulated in terms of the principal values of the right stretch tensor. Incompressibility is fulfilled exactly using the plane stress constraint. Furthermore, a finite element formulation of the Membrane Theory is given. The use of the tangential stiffness matrix, derived analytically, provides a quadratically convergent solution process. Several numerical examples show the robustness of the developed finite element.