Remarks on elastic buckling for sectorial plates

This work investigates the edge-buckling experienced by a sectorial plate in a uniform bi-axial state of stress and subject to in-plane bending. Since the governing differential equations have variable coefficients, it turns out that the neutrally stable eigenfunctions can be qualitatively quite different as the mode number varies. Our interactive boundary-layer analysis succeeds in capturing the most dangerous mode associated with the global minimum of the marginal stability curve, while a complementary WKB route supplies an explanation for the morphological transitions experienced by the eigenmodes. The validity of our analysis is confirmed by direct numerical simulations of the full fourth-order buckling equation, which are in excellent agreement with the theoretical considerations.     

Oval test coil for examining mechanical effects in superconducting coils

A method of investigating mechanical effects in superconducting coils has been demonstrated using an oval magnet constructed to produce high mechanical stress in a portion of a small test coil. The oval shape is maintained by an internal longitudinal strut which may be used to prestress the winding and control the longitudinal deformation. Lateral and longitudinal deflections during energization are monitored by linear variable differential transformers. Initial results show very complex deflection patterns, particularly at low field. There are indications of diamagnetic behaviour of the composite twisted multifilamentary conductor below Hc₁ and of possible conductor slippage but much remains unexplained.     

A variational approach to magnetoelastic buckling problems for systems of superconducting tori

A variational principle for the magnetoelastic stability problem of superconductors is constructed. Independently, a pair of integral equations is derived, from which the initial and the perturbed field can be computed. The integral equations are solved for in-plane buckling of a slender pair of concentric tori, and out-of-plane buckling of a slender pair of equal coaxial tori. By using the variational principle, it is shown that both cases can become unstable when the currents on the two tori are equally directed, and the pertinent buckling values are calculated. The thus obtained buckling values are compared with the results of an alternative, mathematically less rigorous, method. A good correspondence between the two methods is found (at least as long as the two tori are not too near).     

System for coil simulation measurements of losses and instabilities in superconducting wires

A new system for measuring ac losses in superconductors under coil simulation conditions is described. It is aimed to investigate instabilities in local points of a coil. Currents up to 150 A and magnetic fields up to 0.4 T can be applied simultaneously and can be varied independently. The magnetic and electric fields on both sides of the sample are measured by means of pick-up coils and potential leads, respectively. By this method the instantaneous values of the power introduced through each of both sample surfaces can be measured separately. The validity of the method and the performance of the system are demonstrated by measuring the losses of a copper-clad single-core Nb-Ti-Zr wire for several values of the ratio between the current and the magnetic field, which are inphase.     

System for coil simulation measurements of losses and instabilities in superconducting wires

A new system for measuring ac losses in superconductors under coil simulation conditions is described. It is aimed to investigate instabilities in local points of a coil. Currents up to 150 A and magnetic fields up to 0.4 T can be applied simultaneously and can be varied independently. The magnetic and electric fields on both sides of the sample are measured by means of pick-up coilds and potential leads, respectively. By this method the instantaneous values of the power introduced through each of both sample surfaces can be measured separately. The validity of the method and the performance of the system are demonstrated by measuring the losses of a copper-clad single-core Nb---Ti---Zr wire for several values of the ratio between the current and the magnetic field, which are inphase.     

A superconducting coil indirectly cooled by forced helium flow

A small superconducting coil is indirectly cooled by a forced flow of helium. The coil, wound from Nb-Ti-Zr multifilament superconducting composite, is 15 mm id, 24 mm od and 30 mm long. The maximum central field is 30.3 kG at 4.2 K. Contact between the cooling tube and the coil is achieved using grease.The experimental results are expressed by a relation of critical current and energizing rate. Typical transient temperatures of the coil and coolant during energizing and after quenching are presented.The analysis shows the design of coils of this type is possible using hysteresis loss and heat conduction analysis.     

Study on cross section of high temperature superconducting coil

It is in particular of importance for HTS coils to secure a larger central magnetic field and/or a large stored energy with shorter length of HTS tapes. The critical current of an HTS tape depends on both the flux density and the flux angle against tapes. From this point, the performance improvement of HTS coils is taken into account with an analytical model. The minimum volume coil derived from the Fabry Factor constant curve is taken concerning the original coil shape, which is often employed in low temperature superconducting coils. The coil critical current was analyzed in consideration of the anisotropic properties of the tape.The electric field of HTS tapes in the coil was calculated at the coil critical current and the high electric field portion were cut out. The optimal coil cross section is obtained by iterating this calculation process. As a result, the critical current and the stored energy density of the coil were improved. The stored energy density increased about 17% and the central magnetic field was almost kept constant regardless of 19% reduction of HTS tapes, as compared with the original coil with the rectangular cross section.     

Probabilistic bounds on effective elastic moduli for the superconducting coils

The main purpose of the paper presented is probabilistic characterization of the effective elastic characteristics of a superconducting four-component composite. The probabilistic moments of these characteristics up to the fourth-order have been estimated on the basis of experimentally measured expected values and standard deviations of component materials elastic properties (Young moduli and Poisson coefficients). The Monte-Carlo simulation technique has been used to carry out all computational experiments. The results computed have been discussed in details in order to verify the sensitivity of respective probabilistic moments to input random data and to total number of random trials used to estimate these values.     

Collective buckling of an elastic beam array on an elastic substrate for applications in soft lithography

We analyze the collective buckling of an array of vertical elastic beams with their lower ends built into an elastic substrate. The beams interact between themselves through the deformation of the elastic substrate. The present analysis is more sophisticated than previous ones on rigid beams on an elastic substrate in that the beams are regarded as elastic rather than rigid. From the linear theory for elastic beam buckling and the linear theory of elasticity, an eigenvalue problem is formulated and solved. Calculations show that the deformability of the beams lowers the critical height of the beams, but it does not affect the buckling pattern much. Our work also suggests that the collective buckling is dominated by the interaction of neighboring beams through the deformation of the substrate rather than whether the beams are rigid or elastic. The results are useful for the better understanding, design and application of the nanostructures produced by soft lithography.     

Torsional buckling of elastic cylinders with hard coatings

The torsional buckling characteristic of an elastic cylinder with a hard surface coating layer is addressed in this paper. Deformations of the core and surface layer are obtained analytically through the Navier??s equation and thin shell model, respectively. Both infinitely and finitely long cylinders are studied and the effects of the surface layer??s stiffness, thickness, residual stresses, as well as the cylinder lengths on the critical torsional angle and buckling morphologies, are discussed. It is found that either the surface rippling or global buckling mode may occur when there exist residual stresses within the surface layer. The critical torsional angle increases when the surface layer becomes stiffer and thinner. In addition, higher-order rippling modes frequently occur for a finite-length cylinder with stiffer and thinner surface layer.     

Global buckling load of a nonlinearly elastic bar

Summary The nonlinear buckling of an elastic bar with softening characteristic is studied. It is found that, under large disturbances, the bar may buckle under loads well below the linear buckling load.     

On buckling of crosswise rigid elastic cantilever plates

Summary The classical two-dimensional equations for the buckling of thin elastic anisotropic plates are reduced, on the basis of an assumption of crosswise rigidity, to a system of one-dimensional equations. The reduction pre-supposes that the crosswise dimension of the plate is small compared to it's spanwise dimension and leads, effectively, to a system of beam buckling equations which automatically associates a warping stiffness effect with the classical beam bending and twisting stiffness effects. In the event that inertia load terms are to be considered the system is of the eight order with respect to the spanwise space coordinate. In the absence of such load terms the system can be reduced to the sixth order, with further reductions possible for suitably specialized load conditions.     

A variational approach to magneto-elastic buckling problems for systems of ferromagnetic or superconducting beams

Based upon a variational principle derived in a preceding paper, expressions for the magneto-elastic buckling values for ferromagnetic or superconducting systems are given. These relations are evaluated for systems of slender beams. Explicit buckling values are calculated for a single ferromagnetic or superconducting beam of arbitrary cross-section, and for systems of two parallel ferromagnetic or superconducting rods. In the analysis needed for the calculation of the intermediate (i.e., rigid-body) and the perturbed magnetic fields, an intensive use of methods inherent in the theory of complex functions is made. In conclusion our results for a set of two superconducting rods are compared with the results of a mathematically less complicated, but also less rigorous, theory.     

A boundary element method for elastic buckling analysis of assembled plate structures

In this paper, we first discuss the integral equation formulation for the buckling problem of a single plate, using the biharmonic fundamental solution for the plate bending problems. The so called boundary-element method previously proposed by the senior author is applied to the numerical solution of the resulting set of integral equations. The total set of simultaneous equations are derived for nodal unknowns taken out of the whole domain, and reduced to an algebraic set of eigenvalue equations. The proposed method is method to the solution of elastic buckling of assembled plate structures. A few examples are computed and results obtained are compared with other solutions to demonstrate the potential usefulness of the proposed method.     

Edge-wave buckling of rolled elastic strips: asymptotic results

The problem considered in this paper concerns the edge-wave buckling phenomenon commonly encountered in forming processes such as rolling and levelling. Due to the combined action of global tensile forces and residual stresses, the elastic strips involved in these scenarios experience a symmetric short-wave deformation pattern that tends to be confined near their long edges. We use boundary-layer techniques to provide simple estimates for the critical load and the wavelength of the buckling waves. A number of complementary asymptotic features of the marginal stability curves are also reported.     

Analysis of the elastic buckling of a plywood column

Buckling tests were conducted on specimens of 5-ply lauan plywood for a range of slenderness ratios to measure its buckling stress. Three-dimensional finite element calculations of buckling stress were performed and their validity examined by comparison with experimental results. Both experimental and calculated results revealed that buckling stress is influenced by Young’s modulus values (a measure of stiffness) obtained not only under flexural loading but also under axial loading. When the axial Young’s modulus is larger than the flexural Young’s modulus, the buckling stress is measured as larger than that obtained using the flexural Young’s modulus alone. Inversely, when the axial Young’s modulus is smaller than the flexural Young’s modulus, the buckling stress is measured as smaller than that obtained using the flexural Young’s modulus alone. Therefore, both the Young’s modulus values should be taken into account for determining the buckling stress of a plywood column.     

超导线圈的等效热膨胀系数的理论与实验研究

给出了计算超导线圈等效热膨胀率的理论模型和计算方法,对比了各种测量材料线膨胀系数的实验方法,并且给出了低温应变片测量热膨胀系数的技术原理.采用低温应变片法测量了矩形截面导线缠绕成型的超导线圈由77 K到300 K的线膨胀系数,并将实验测试结果与理论计算结果进行了对比分析.