Abstract:We present a new method for the design of devices to manipulate the displacement field in Elastic materials. It consists of solving a nonlinear optimization problem where the objective function defines the error in matching a desired displacement field, and the design variables determine the required material distribution within the device. In order to facilitate fabrication, the material at a given point of the device is chosen from a set of predefined materials, giving raise to a discrete optimization proble… Show more
“…Wang et al's design configuration, for a plate with central circular hole under displacement loading, achieved a 4% difference in directional spatial displacement fields when cloaked, compared to 17.2% when uncloaked [21]. Optimization-based design by Fachinotti et al [22] presented a device to manipulate displacement fields on a structure under uniaxial compression loading. Fachinotti et al plotted displacement fields for both homogeneous plates and plates with a cloaked hole.…”
The presence of a central cutout in thin, plate-like structures often results in a reduction in load-carrying capacity due to a removal of bending stiffness at the unsupported central region. This paper presents a design approach that minimizes the mechanically detrimental effect of a central circular cutout on the buckling performance of a flat, square, simply supported plate under uniaxial compression, for a hole diameter-to-plate-width ratio of 𝐷/𝑙 𝑦 = 0.3. We consider the potential design of a holed laminated plate to have the performance of an unholed target design by application of the variable-angle Continuous Tow Shearing (CTS) process to generate periodic stiffness variations, in order to significantly disrupt and redirect prebuckling stresses. Parallelized population-based optimization approaches are used to find structural solutions which can meet the target unholed plate performance with lowest mass increase. Both holed straight fiber and fiber-steered designs are found which give near-identical structural performance to an optimum unholed eight-ply straight fiber plate of square aspect ratio ([±45] 2s ). The holed eight-ply straight fiber plate gives near identical prebuckling stiffness and within ±3% buckling load of the holed plate for a 21% mass increase where plylevel orientations ([±79/±54] s ) and ply-level thicknesses ([(1.22𝑡 0 ) 2 /(1.37𝑡 0 ) 2 ] s ) are allowed to vary. Comparatively, the eight-ply holed CTS fiber-steered plate ([±90⟨33|21⟩ 10 /±90⟨52|2⟩ 4 ] s ) achieves within 1% of the prebuckling stiffness and ±1% of the buckling load of the target unholed plate for a 9% mass increase. Stress analysis is conducted to identify the governing mechanics that account for the improved performance of the CTS fiber steered plate. We find that the fiber-steered solution removes high-magnitude stresses away from the hole boundary to a region of higher stiffness within the plate, which are produced by the fiber angle-ply thickness coupling of the CTS process. Overall, the findings of the present work indicate a suitable direction for future research and the need to further investigate the non-intuitive mechanics arising from CTS fiber steering for application to future aerostructural research and development.
“…Wang et al's design configuration, for a plate with central circular hole under displacement loading, achieved a 4% difference in directional spatial displacement fields when cloaked, compared to 17.2% when uncloaked [21]. Optimization-based design by Fachinotti et al [22] presented a device to manipulate displacement fields on a structure under uniaxial compression loading. Fachinotti et al plotted displacement fields for both homogeneous plates and plates with a cloaked hole.…”
The presence of a central cutout in thin, plate-like structures often results in a reduction in load-carrying capacity due to a removal of bending stiffness at the unsupported central region. This paper presents a design approach that minimizes the mechanically detrimental effect of a central circular cutout on the buckling performance of a flat, square, simply supported plate under uniaxial compression, for a hole diameter-to-plate-width ratio of 𝐷/𝑙 𝑦 = 0.3. We consider the potential design of a holed laminated plate to have the performance of an unholed target design by application of the variable-angle Continuous Tow Shearing (CTS) process to generate periodic stiffness variations, in order to significantly disrupt and redirect prebuckling stresses. Parallelized population-based optimization approaches are used to find structural solutions which can meet the target unholed plate performance with lowest mass increase. Both holed straight fiber and fiber-steered designs are found which give near-identical structural performance to an optimum unholed eight-ply straight fiber plate of square aspect ratio ([±45] 2s ). The holed eight-ply straight fiber plate gives near identical prebuckling stiffness and within ±3% buckling load of the holed plate for a 21% mass increase where plylevel orientations ([±79/±54] s ) and ply-level thicknesses ([(1.22𝑡 0 ) 2 /(1.37𝑡 0 ) 2 ] s ) are allowed to vary. Comparatively, the eight-ply holed CTS fiber-steered plate ([±90⟨33|21⟩ 10 /±90⟨52|2⟩ 4 ] s ) achieves within 1% of the prebuckling stiffness and ±1% of the buckling load of the target unholed plate for a 9% mass increase. Stress analysis is conducted to identify the governing mechanics that account for the improved performance of the CTS fiber steered plate. We find that the fiber-steered solution removes high-magnitude stresses away from the hole boundary to a region of higher stiffness within the plate, which are produced by the fiber angle-ply thickness coupling of the CTS process. Overall, the findings of the present work indicate a suitable direction for future research and the need to further investigate the non-intuitive mechanics arising from CTS fiber steering for application to future aerostructural research and development.
“…Such an annular device allows the redirection of the electromagnetic field to surround the object, while also remains unperturbed outside the metamaterial region. Important achievements in electromagnetic cloaking were made for both microwave and optical frequencies, and such ideas were successfully extended to other fields, such as thermodynamics, acoustics, and mechanics . In the case of heat‐transfer problems, the key to achieve invisibility is also the heat conduction equation invariance under curvilinear transformations …”
Section: Invisibility and Camouflagementioning
confidence: 99%
“…Important achievements in electromagnetic cloaking were made for both microwave [26][27][28] and optical frequencies, [29][30][31][32][33][34][35][36][37][38][39] and such ideas were successfully extended to other fields, [40] such as thermodynamics, [1,[13][14][15][41][42][43][44][45][46][47][48][49] acoustics, [50][51][52][53] and mechanics. [54][55][56][57] In the case of heat-transfer problems, the key to achieve invisibility is also the heat conduction equation invariance under curvilinear transformations. [58,59]…”
Progress in material science has allowed the control of different physical fields in a manner that would be unachievable with ordinary materials. The development of engineered materials (the so‐called metamaterials) to control the conductive heat flux has revolutionized the manner of manipulating thermal energy and allowed the possibility of guiding the heat flux in ways difficult to accept for human intuition. Herein, a brief review regarding the recent progress and developments in thermal metamaterials conceived to perform several conductive heat flux manipulation tasks is provided. Deeply theoretical discussions concerning design methodologies are left a side, and the focus is made on the design and manufacturing feasibility of metamaterials for thermal cloaking and camouflage, heat flux concentration, and inversion, among other applications that lead to the next generation of thermal devices.
“…The elliptic equations governing elastostatics are not form-invariant under coordinate transformations [11]; thus, far fewer attempts have been made to achieve elastostatic cloaking [16,17]. Topology optimization has been pursued for elastostatic cloak design [18,19], but a formulation in the discrete setting that is capable of achieving multi-directional elastostatic cloaking devices that mitigate the influence of circular or elliptical holes has not been fully explored. Figure 1Elastostatic cloak design in 2D lattices: ( a ) reference lattice; ( b ) lattice with a prescribed circular hole surrounded by a region in which a cloak should be designed; ( c ) lattice in which the cloak geometry is defined by a coordinate transformation of the reference lattice nodes.…”
An optimization-based approach is proposed to design elastostatic cloaking devices in two-dimensional (2D) lattices. Given an elastic lattice with a defect, i.e. a circular or elliptical hole, a small region (cloak) around the hole is designed to hide the effect of the hole on the elastostatic response of the lattice. Inspired by the direct lattice transformation approach to elastostatic cloaking in 2D lattices, the lattice nodal positions in the design region are obtained using a coordinate transformation of the reference (undisturbed) lattice nodes. Subsequently, additional connectivity (i.e. a ground structure) is defined in the design region and the stiffness properties of these elements are optimized to mimic the global stiffness characteristics of the reference lattice. A weighted least-squares objective function is proposed, where the weights have a physical interpretation—they are the design-dependent coefficients of the design lattice stiffness matrix. The formulation leads to a convex objective function that does not require a solution to an additional adjoint system. Optimization-based cloaks are designed considering uniaxial tension in multiple directions and are shown to exhibit approximate elastostatic cloaking, not only when subjected to the boundary conditions they were designed for but also for uniaxial tension in directions not used in design and for shear loading.
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