K. Seffen - Academia.edu (original) (raw)
Papers by K. Seffen
International Journal of Solids and Structures, 2009
International Journal of Solids and Structures, 2019
Journal of Applied Mechanics
The “carpenter’s measuring tape” is a thin spring-steel strip, preformed to a curved cross sectio... more The “carpenter’s measuring tape” is a thin spring-steel strip, preformed to a curved cross section of radius R, which is straight when being used for measuring. Under bending moments, it forms a localized hinge, in which the transverse curvature is suppressed, and the longitudinal radius r is approximately equal to R. Rimrott made a simple strain energy analysis of the hinge region for isotropic material, which predicted that r = R. Both experimental observations and finite element computations show that ξ = r/R > 1, where the value of ξ exceeds unity by up to 15%, depending on whether the tape is bent in “equal-sense” or “opposite-sense” curvature; ξ varies linearly with Poisson’s ratio in both cases. We make a minor change to Rimrott’s analysis by introducing a boundary layer, in order better to satisfy the physical conditions at the free edges; this successfully accounts for the observed behavior of the tape.
Royal Society Open Science
We investigate stabilizing and eschewing factors on bistability in polar-orthotropic shells in or... more We investigate stabilizing and eschewing factors on bistability in polar-orthotropic shells in order to enhance morphing structures. The material law causes stress singularities when the circumferential stiffness is smaller than the radial stiffness ( β < 1), requiring a careful choice of the trial functions in our Ritz approach, which employs a higher-order geometrically nonlinear analytical model. Bistability is found to strongly depend on the orthotropic ratio, β , and the in-plane support conditions. An investigation of their interaction offers a new perspective on the effect of the hoop stiffness on bistability: while usually perceived as promoting, it is shown to be only stabilizing insofar as it prevents radial expansions; however, if in-plane supports are present, it becomes a redundant feature. Closed-form approximations of the bistable threshold are then provided by single-curvature-term approaches. For significantly stiffer values of the radial stiffness, a strong coup...
Proceedings of the Royal Society A: Mathematical, Physical and Engineering Science
Multistable shells are thin-walled structures that have more than one stable state of self-stress... more Multistable shells are thin-walled structures that have more than one stable state of self-stress. We consider isotropic axisymmetrical shallow shells of arbitrary polynomial shapes using a Föppl–von Kármán analytical model. By employing a Rayleigh–Ritz approach, we identify stable shapes from local minima in the strain energy formulation, and we formally characterize the level of influence of the boundary conditions on the critical geometry for achieving bistable inversion—an effect not directly answered in the literature. Systematic insight is afforded by connecting the boundary to ground through sets of extensional and rotational linear springs. For typical cap-like shells, it is shown that bistability is generally enhanced when the extensional spring stiffness increases and when the rotational spring stiffness decreases, i.e. when boundary movements in-plane are resisted but when their rotations are not; however, for certain other shapes and large in-plane stiffness values, bist...
The Aeronautical Journal, 2009
Future space telescopes will be required to have significantly greater aperture and lower areal d... more Future space telescopes will be required to have significantly greater aperture and lower areal density than is currently achievable. Gossamer spacecraft structures have been proposed as a means of achieving this, but the technologies are far from mature. A state-of-the-art review is timely and necessary as new structural paradigms are being considered for the next generation of space telescopes. There is, however, a knowledge gap between the structural engineering community and the additional fields involved in the complete telescope system, leading to the proposal of structures which are unlikely to be launched. It is hoped that, by providing a resource by which structural engineers are made aware of the wider issues in telescope design, this review will serve to overcome this knowledge gap to facilitate productive collaboration.
The Aeronautical Journal, 2006
The conditions for thermally-induced buckling of an unloaded thin, circular disk are compared fro... more The conditions for thermally-induced buckling of an unloaded thin, circular disk are compared from two well-known but unconnected studies: an approximate solution by Freund for a constant thickness disk, which must neglect the free edge condition, and an exact solution by Mansfield but only for a disk whose thickness tapers to zero in a particular manner. It is shown that buckling occurs at slightly higher values compared to a finite element analysis of a constant thickness disk but that the case of variable thickness seems to offer a closer result, which suggests that it better models the boundary layer behaviour near the free edge.
Physical Review Applied, 2015
45th AIAA/ASME/ASCE/AHS/ASC Structures, Structural Dynamics & Materials Conference, 2004
This study is concerned with novel bi-stable structures, which are proposed for enabling reconfig... more This study is concerned with novel bi-stable structures, which are proposed for enabling reconfigurable structures with multiple, load-free equilibrium states. The first structure is a discrete member bi-stable module and is deformable in shear. The degree of shape change is predicted by a compatibility analysis. The stiness of the module in either state is confirmed by a modified version of Maxwell’s Rule for planar frameworks. The stiness and degree of stability of larger grid-like structures formed by interconnecting modules is also considered. The second structure is a shallow, continuous dome pressed into a thin sheet, which can be inverted by snapping through the sheet. Multiply stable shells are formed by stamping many domes in an ordered array into the complete sheet. It is shown that residual stresses are responsible for the novel, large and stable deformations, and a finite element analysis is performed to investigate the eects of the forming process upon the inversion behaviour of a single dome. I. Introduction In this paper, novel bi-stable structures are proposed for developing reconfigurable structures. The latter may be defined as a class of structures whose topology and/or shape can be altered appreciably and fixated, in order to increase their functionality and/or to enhance their performance capabilities. Deployable spacecraft structures (Pellegrino 1 ), for example, embrace both principles: their mechanistic properties permit them to be folded for stowage during transportation and to be unfolded in the first stages of deployment; they are then made sti at the end of deployment for structural integrity during operation. An alternative solution uses structures that have multiple but stable, i.e. positively sti, equilibrium states. The transition between states during reconfiguration must be enabled by higher than normal loads either applied externally or reacted internally by integrated actuators. Hence, the simplest reconfigurable structure exhibits bi-stability, and this paper introduces the behaviour of two, rather dierent concepts, which may be assembled or formed together into larger, multiply stable structures. The first concept is a pin-jointed structure although here, simple models are made from cardboard strips with frictional hinges. It has a large-displacement shearing mode and “snaps” elastically into one of two stable, free-standing configurations, as predicted by an elementary compatibility analysis. The well-known Maxwell criterion is modified to give the determinacy of the structure, and is confirmed by a mobility analysis. The method can be applied to modular grids formed by interconnecting structures to elucidate possible modes of deformation. Depending on the tessellation of structures, local, as well as global modes are possible, and simpler bi-stable structures can be found within the general layout. The second concept is a continuous, shallow axi-symmetric dome that has been pressed into hardened, flat metal sheet. The dome can be made to invert and revert by “popping” it through the sheet in either direction. The area surrounding the dome no longer remains flat by virtue of its interaction with the dome at its rim. When an array of closely-spaced domes is formed over the entire sheet, individual domes can be pushed through singly, or in localised rows and columns, and their interaction with each other creates multiple, global distortions. When all domes are in the same sense, in either direction, the sheet can adopt one of several cylindrical forms. It is shown that residual stresses are largely responsible, and is verified by novel experiments; a finite element analysis of the dome formation is then detailed.
International Journal of Mechanical Engineering Education, 2002
Research into smart structures is now extensive and, increasingly, is finding practical applicati... more Research into smart structures is now extensive and, increasingly, is finding practical application in many aerospace, mechanical-, civil-, and bio-engineering domains. Thus, to maintain pace with well-established developments, it is inevitable that analysis of smart structures finds a place in engineering degree courses. The examples studied here provide an introduction and are elementary beams with perfectly bonded layers of piezoelectric material. Simple analytical models describe the induced stress and deformation in each beam according to compact dimensionless groups. A finite element analysis is also carried out to confirm results and the sensitivity of behaviour due to the mesh density is addressed.
45th AIAA/ASME/ASCE/AHS/ASC Structures, Structural Dynamics & Materials Conference, 2004
This study is concerned with multiply coiled, hierarchical structures, known formally as hyperhel... more This study is concerned with multiply coiled, hierarchical structures, known formally as hyperhelices, for use as large displacement, solid-state actuators. They are made by curving thin strips of active material into successively larger helicoidal forms. The degree of shape change for any hyperhelix is obtained from the recursive solution of a pair of governing equations of deformation, and it is shown that the activated deformations on the original strip are greatly amplified in terms of the displacements output in the overall structure. Practical hyperhelices are coils and coiled-coils, and are made from piezoelectric ceramic and bi-metallic materials. It is shown that experimental results accurately correlate to predictions from the theoretical approach.
International Journal of Mechanical Engineering Education, 2001
Journal of Materials Science, 2002
Piezoelectric actuators tend to be made from relatively simple shapes such as blocks, plates and ... more Piezoelectric actuators tend to be made from relatively simple shapes such as blocks, plates and beams. These shapes allow for a range of displacements from key actuation modes but, in order to expand this range, complex structures are required that cannot be made via conventional means. This study presents a novel manufacturing method for such structures using a green ceramic
Journal of Engineering Mechanics, 2008
Journal of Applied Mechanics, 2001
Journal of Applied Mechanics, 2014
Journal of Applied Mechanics, 2013
Solid Mechanics and Its Applications, 2002
International Journal of Solids and Structures, 2009
International Journal of Solids and Structures, 2019
Journal of Applied Mechanics
The “carpenter’s measuring tape” is a thin spring-steel strip, preformed to a curved cross sectio... more The “carpenter’s measuring tape” is a thin spring-steel strip, preformed to a curved cross section of radius R, which is straight when being used for measuring. Under bending moments, it forms a localized hinge, in which the transverse curvature is suppressed, and the longitudinal radius r is approximately equal to R. Rimrott made a simple strain energy analysis of the hinge region for isotropic material, which predicted that r = R. Both experimental observations and finite element computations show that ξ = r/R > 1, where the value of ξ exceeds unity by up to 15%, depending on whether the tape is bent in “equal-sense” or “opposite-sense” curvature; ξ varies linearly with Poisson’s ratio in both cases. We make a minor change to Rimrott’s analysis by introducing a boundary layer, in order better to satisfy the physical conditions at the free edges; this successfully accounts for the observed behavior of the tape.
Royal Society Open Science
We investigate stabilizing and eschewing factors on bistability in polar-orthotropic shells in or... more We investigate stabilizing and eschewing factors on bistability in polar-orthotropic shells in order to enhance morphing structures. The material law causes stress singularities when the circumferential stiffness is smaller than the radial stiffness ( β < 1), requiring a careful choice of the trial functions in our Ritz approach, which employs a higher-order geometrically nonlinear analytical model. Bistability is found to strongly depend on the orthotropic ratio, β , and the in-plane support conditions. An investigation of their interaction offers a new perspective on the effect of the hoop stiffness on bistability: while usually perceived as promoting, it is shown to be only stabilizing insofar as it prevents radial expansions; however, if in-plane supports are present, it becomes a redundant feature. Closed-form approximations of the bistable threshold are then provided by single-curvature-term approaches. For significantly stiffer values of the radial stiffness, a strong coup...
Proceedings of the Royal Society A: Mathematical, Physical and Engineering Science
Multistable shells are thin-walled structures that have more than one stable state of self-stress... more Multistable shells are thin-walled structures that have more than one stable state of self-stress. We consider isotropic axisymmetrical shallow shells of arbitrary polynomial shapes using a Föppl–von Kármán analytical model. By employing a Rayleigh–Ritz approach, we identify stable shapes from local minima in the strain energy formulation, and we formally characterize the level of influence of the boundary conditions on the critical geometry for achieving bistable inversion—an effect not directly answered in the literature. Systematic insight is afforded by connecting the boundary to ground through sets of extensional and rotational linear springs. For typical cap-like shells, it is shown that bistability is generally enhanced when the extensional spring stiffness increases and when the rotational spring stiffness decreases, i.e. when boundary movements in-plane are resisted but when their rotations are not; however, for certain other shapes and large in-plane stiffness values, bist...
The Aeronautical Journal, 2009
Future space telescopes will be required to have significantly greater aperture and lower areal d... more Future space telescopes will be required to have significantly greater aperture and lower areal density than is currently achievable. Gossamer spacecraft structures have been proposed as a means of achieving this, but the technologies are far from mature. A state-of-the-art review is timely and necessary as new structural paradigms are being considered for the next generation of space telescopes. There is, however, a knowledge gap between the structural engineering community and the additional fields involved in the complete telescope system, leading to the proposal of structures which are unlikely to be launched. It is hoped that, by providing a resource by which structural engineers are made aware of the wider issues in telescope design, this review will serve to overcome this knowledge gap to facilitate productive collaboration.
The Aeronautical Journal, 2006
The conditions for thermally-induced buckling of an unloaded thin, circular disk are compared fro... more The conditions for thermally-induced buckling of an unloaded thin, circular disk are compared from two well-known but unconnected studies: an approximate solution by Freund for a constant thickness disk, which must neglect the free edge condition, and an exact solution by Mansfield but only for a disk whose thickness tapers to zero in a particular manner. It is shown that buckling occurs at slightly higher values compared to a finite element analysis of a constant thickness disk but that the case of variable thickness seems to offer a closer result, which suggests that it better models the boundary layer behaviour near the free edge.
Physical Review Applied, 2015
45th AIAA/ASME/ASCE/AHS/ASC Structures, Structural Dynamics & Materials Conference, 2004
This study is concerned with novel bi-stable structures, which are proposed for enabling reconfig... more This study is concerned with novel bi-stable structures, which are proposed for enabling reconfigurable structures with multiple, load-free equilibrium states. The first structure is a discrete member bi-stable module and is deformable in shear. The degree of shape change is predicted by a compatibility analysis. The stiness of the module in either state is confirmed by a modified version of Maxwell’s Rule for planar frameworks. The stiness and degree of stability of larger grid-like structures formed by interconnecting modules is also considered. The second structure is a shallow, continuous dome pressed into a thin sheet, which can be inverted by snapping through the sheet. Multiply stable shells are formed by stamping many domes in an ordered array into the complete sheet. It is shown that residual stresses are responsible for the novel, large and stable deformations, and a finite element analysis is performed to investigate the eects of the forming process upon the inversion behaviour of a single dome. I. Introduction In this paper, novel bi-stable structures are proposed for developing reconfigurable structures. The latter may be defined as a class of structures whose topology and/or shape can be altered appreciably and fixated, in order to increase their functionality and/or to enhance their performance capabilities. Deployable spacecraft structures (Pellegrino 1 ), for example, embrace both principles: their mechanistic properties permit them to be folded for stowage during transportation and to be unfolded in the first stages of deployment; they are then made sti at the end of deployment for structural integrity during operation. An alternative solution uses structures that have multiple but stable, i.e. positively sti, equilibrium states. The transition between states during reconfiguration must be enabled by higher than normal loads either applied externally or reacted internally by integrated actuators. Hence, the simplest reconfigurable structure exhibits bi-stability, and this paper introduces the behaviour of two, rather dierent concepts, which may be assembled or formed together into larger, multiply stable structures. The first concept is a pin-jointed structure although here, simple models are made from cardboard strips with frictional hinges. It has a large-displacement shearing mode and “snaps” elastically into one of two stable, free-standing configurations, as predicted by an elementary compatibility analysis. The well-known Maxwell criterion is modified to give the determinacy of the structure, and is confirmed by a mobility analysis. The method can be applied to modular grids formed by interconnecting structures to elucidate possible modes of deformation. Depending on the tessellation of structures, local, as well as global modes are possible, and simpler bi-stable structures can be found within the general layout. The second concept is a continuous, shallow axi-symmetric dome that has been pressed into hardened, flat metal sheet. The dome can be made to invert and revert by “popping” it through the sheet in either direction. The area surrounding the dome no longer remains flat by virtue of its interaction with the dome at its rim. When an array of closely-spaced domes is formed over the entire sheet, individual domes can be pushed through singly, or in localised rows and columns, and their interaction with each other creates multiple, global distortions. When all domes are in the same sense, in either direction, the sheet can adopt one of several cylindrical forms. It is shown that residual stresses are largely responsible, and is verified by novel experiments; a finite element analysis of the dome formation is then detailed.
International Journal of Mechanical Engineering Education, 2002
Research into smart structures is now extensive and, increasingly, is finding practical applicati... more Research into smart structures is now extensive and, increasingly, is finding practical application in many aerospace, mechanical-, civil-, and bio-engineering domains. Thus, to maintain pace with well-established developments, it is inevitable that analysis of smart structures finds a place in engineering degree courses. The examples studied here provide an introduction and are elementary beams with perfectly bonded layers of piezoelectric material. Simple analytical models describe the induced stress and deformation in each beam according to compact dimensionless groups. A finite element analysis is also carried out to confirm results and the sensitivity of behaviour due to the mesh density is addressed.
45th AIAA/ASME/ASCE/AHS/ASC Structures, Structural Dynamics & Materials Conference, 2004
This study is concerned with multiply coiled, hierarchical structures, known formally as hyperhel... more This study is concerned with multiply coiled, hierarchical structures, known formally as hyperhelices, for use as large displacement, solid-state actuators. They are made by curving thin strips of active material into successively larger helicoidal forms. The degree of shape change for any hyperhelix is obtained from the recursive solution of a pair of governing equations of deformation, and it is shown that the activated deformations on the original strip are greatly amplified in terms of the displacements output in the overall structure. Practical hyperhelices are coils and coiled-coils, and are made from piezoelectric ceramic and bi-metallic materials. It is shown that experimental results accurately correlate to predictions from the theoretical approach.
International Journal of Mechanical Engineering Education, 2001
Journal of Materials Science, 2002
Piezoelectric actuators tend to be made from relatively simple shapes such as blocks, plates and ... more Piezoelectric actuators tend to be made from relatively simple shapes such as blocks, plates and beams. These shapes allow for a range of displacements from key actuation modes but, in order to expand this range, complex structures are required that cannot be made via conventional means. This study presents a novel manufacturing method for such structures using a green ceramic
Journal of Engineering Mechanics, 2008
Journal of Applied Mechanics, 2001
Journal of Applied Mechanics, 2014
Journal of Applied Mechanics, 2013
Solid Mechanics and Its Applications, 2002