A new load-dependent Ritz vector method for structural dynamics analyses: quasi-static Ritz vectors

Existing load-dependent Ritz vector (LDRV) methods employ static recurrence procedures to generate the Ritz vectors. As such, these vector methods are best suited for low-frequency problems. For higher-frequency problems, the existing methods may engender large sets of Ritz vectors, which significantly reduces the methods’ efficiency. A new algorithm is presented for LDRV generation using a quasi-static recurrence procedure, denoted as the quasi-static Ritz vector (QSRV) method. A tuning parameter, designated as the centering frequency, controls the behavior of the QSRV approach, enabling the new method to improve upon existing LDRV methods for particular frequency ranges of interest. Compared with existing LDRV methods, the QSRV method is more efficient (in terms of the number of Ritz vectors), more accurate (in terms of response errors), and more stable (in terms of orthogonality). Numerical examples are provided to illustrate the accuracy, efficiency and generality of the proposed method.     

含盐体系汽液平衡的测定方法和测定仪器的研究

针对含盐体系汽液平衡测定的特点及常用测定仪器和方法中的问题，改制了具有沸点仪和双循环平衡釜双重功能CS－Ⅱ型VLE测定仪，并以拟表态法测定了含盐体系汽液平衡的泡点线和平衡液相恒盐浓度下的露点线，新测定仪能避免用双循环仪器时极易出现的流动不稳定性和爆沸现象，成功地测定了氯化钙平衡液相浓度为5％的CaCl2-丙酮（1）－甲醇（2）体系的汽液平衡数据。     

Transient lightning responses of grounding systems buried in horizontal multilayered earth with a hybrid method

Combined with the Fast Fourier Transform (FFT), a mathematical hybrid method for accurately computing the lightning response from grounding systems buried in multilayered earth model has been developed in this paper. In the method, electrical circuit consists of “T” typical of basic elements. To accelerate calculations of the method, quasi-static complex image method and closed form of Green's function and analytical formula for mutual induction and impedance coefficients were introduced into this method. With the inverse FFT, the method can be used for studying performances of transient lightning response from the grounding systems.     

Weight function theory and variational formulations for three-dimensional plane elastic cracks advancing

The weight function theory for three-dimensional elastic crack analysis received great attention after the work of Rice (1985, 1989). Several applications have been considered since then, particularly in the context of configurational stability, crack path prediction, stress intensity factor expansions, perturbation approaches. In all cases, a specific hypothesis has been made on the variation of crack shape, in order to formulate the problem in terms of Cauchy principal value. In the present note, such hypothesis is further investigated and consequences discussed. A variational statement given in Salvadori and Fantoni (2013a) is thus rephrased in terms of weight functions. Its discrete formulation shows the potential to accurate approximation of crack front propagation.     

Spatial Stability for the Quasi-Static Problem in Thermoelastic Diffusion Theory

In this paper we derive some spatial stability results for the quasi-static problem in thermoelastic diffusion theory for anisotropic media. The coupled system of equations of thermoelasticity with diffusion is a coupling of an elliptic equation with two parabolic equations. It poses some new mathematical difficulties. Here we study the exponential spatial decay of solutions. An upper bound for the amplitude in terms of the boundary and initial conditions is obtained. The extension of the spatial stability results is also treated.     

Analytical solution of the quasi-static thermoelasticity problem in a pressurized thick-walled cylinder subjected to transient thermal loading

Thermoelasticity problem in a thick-walled cylinder is solved analytically using the finite Hankel transform. Time-dependent thermal boundary conditions are assumed to act on the inner surface of the cylinder. For the mechanical boundary conditions two different cases are assumed: Traction–displacement problem (traction is prescribed on the inner surface and the fixed displacement boundary condition on the outer one) and Traction–Traction problem (tractions are prescribed on both the inner and outer surfaces of the hollow cylinder). The quasi-static solution of the thermoelasticity problem is derived analytically, i.e., the transient thermal response of the cylinder is derived and then, quasi-static structural problem is solved and closed form relations are extracted for the thermal stresses in the two problems. The results show to be in accordance with that cited in the literature in the special cases.     

A study on an axial crush configuration response of thin-wall, steel box components: The quasi-static experiments

An experimental investigation was performed to study a specific axial crush configuration response of steel, square box components under quasi-static testing conditions. For a specific cross-sectional geometry/fabrication process, test specimens were obtained from commercially produced, welded tube lengths of ASTM A36 and ASTM A513 Type 1 plain low-carbon steels and AISI 316 and AISI 304 austenitic stainless steels. Removable grooved caps were used to constrain tube test specimen ends, and collapse initiators in the form of shallow machined grooves were used to control the initial transverse deformations of the test specimen sidewalls. The progressive plastic deformation for all of the test specimens was restricted to the prototype configuration response (fold formation process and the corresponding axial load-axial displacement curve shape) of the symmetric axial crush mode. Crush characteristics were evaluated and, for each material type, observed differences were less than 7% for maximum and minimum load magnitudes and less than 2% for energy absorption, displacement, and mean load quantities in both the initial phase and the secondary folding phase cycles. Overall, results of the study indicate that for a significant range of material strengths, a controlled and repeatable energy absorption process can be obtained for commercially produced steel box components undergoing symmetric axial crush response.     

Partition of initiators in quasi-static precipitation polymerization of AAm/MAc

In order to investigate the partition of initiators for quasi-static precipitation polymerization of acrylamide(AAm) and methacrylic acid(MAc) in ethanol, azo-initiators were employed with various functional groups such as ―COOCH3(V-601, dimethyl 2,2′-azobis(isobutyrate)), ― CN(V-65, 2,2′-Azobis(2,4-diemthylvaleronitrile)), ― COOH(V-501, 4,4′-azobis(4-cyanovaleric acid)) and ―NH-(VA-061, 2,2′-azobis[2-(2-imidazolin-2-yl)propane]), respectively. Particle size, induction time and kinetics of polymerization were investigated by the scanning electron microscopy(SEM) and gravimetry. It was observed that the polymerization parameters, such as the particle size, induction time and polymerization rate, were considerably affected by the functional groups of initiators. Besides, the monomer concentration also played important roles in the particle formation. By using V-601, the polymerization rate was strongly correlated with the total surface area of particles and the concentration of initiators. However, by using V-501, the polymerization rate was strongly related to W0 Ci,0, where W0 is the initial concentration of monomers and Ci,0, the initial concentration of initiators. The results indicated that the different functional groups determined the different partition types of initiators between the minimonomer droplets and the continuous phase due to the molecular interactions of initiator and monomers. V-601 was all partitioned in the continuous phase, but a part of V-65 was partitioned in the minimonomer droplets. Besides the V-501 dissolved in the continuous phase, a part of V-501 was adsorbed on the surface of minimonomer droplets. VA-061 destroyed the stability of minimonomer droplets by the formation of zwitterions with MAA.     

Stress regularity in quasi-static perfect plasticity with a pressure dependent yield criterion

This work is devoted to establishing a regularity result for the stress tensor in quasi-static planar isotropic linearly elastic – perfectly plastic materials obeying a Drucker–Prager or Mohr–Coulomb yield criterion. Under suitable assumptions on the data, it is proved that the stress tensor has a spatial gradient that is locally squared integrable. As a corollary, the usual measure theoretical flow rule is expressed in a strong form using the quasi-continuous representative of the stress.