From Petrov-Einstein-Dilaton-Axion to Navier-Stokes equation in anisotropic model

In this paper we generalize the previous works to the case that the near-horizon dynamics of the Einstein-Dilaton-Axion theory can be governed by the incompressible Navier-Stokes equation via imposing the Petrov-like boundary condition on hypersurfaces in the non-relativistic and near-horizon limit. The dynamical shear viscosity $\eta$ of such dual horizon fluid in our scenario, which isotropically saturates the Kovtun-Son-Starinet (KSS) bound, is independent of both the dilaton field and axion field in that limit.Comment: 13 pages,no figures; v2: 15 page, Equation.(33), some discussions and references added, minor corrections , Version accepted for publication in Physics Letters

A Maxwell-vector p-wave holographic superconductor in a particular background AdS black hole metric

We study the p-wave holographic superconductor for AdS black holes with planar event horizon topology for a particular Lovelock gravity, in which the action is characterized by a self-interacting scalar field nonminimally coupled to the gravity theory which is labeled by an integer $k$. As the Lovelock theory of gravity is the most general metric theory of gravity based on the fundamental assumptions of general relativity, it is a desirable theory to describe the higher dimensional spacetime geometry. The present work is devoted to studying the properties of the p-wave holographic superconductor by including a Maxwell field which nonminimally couples to a complex vector field in a higher dimensional background metric. In the probe limit, we find that the critical temperature decreases with the increase of the index $k$ of the background black hole metric, which shows that a larger $k$ makes it harder for the condensation to form. We also observe that the index $k$ affects the conductivity and the gap frequency of the holographic superconductors.Comment: 14 pages, 6 figure

Design of automotive structural components using high strength sheet steels mechanical properties of materials

INTRODUCTION It is well known that the material properties of steels and the strengths of cold-formed steel members are affected by strain rate. Therefore, the research project sponsored by the American Iron and Steel Institute (AISI) at the University of MIssouri-Rolla during the period from January 1988 through December 1991 was concentrated on a study of the effect of strain rate on mechanical properties of sheet steels and the structural behavior and strength of cold-formed steel members subjected to dynamic loads. Because the previous UMR studies were limited only to the structural members such as stub columns and beams which were assembled with the same material in a given section, the objective of this investigation is to study the structural strength of hybrid automotive structural components using different sheet steels. In this report, two selected sheet steels (25AK and 50SK) were tested to study the effect of strain rate on mechanical properties. The mechanical properties of 25AK and 50SK sheet steels obtained from materials tests will be used later in the evaluation of test results of structural members. A total of 48 tensile coupons and 48 compressive coupons were tested in this phase of study and reported herein. This study was primarily involved with the experimental determination of the dynamic properties of two different sheet steels with nominal static yield strengths of 25 and 50 ksi. The strain rates used 10-4 to 1.0 in./in./sec. All tests were performed at Engineering Research Laboratory of University of Missouri-Rolla by using the MTS 880 test system. In Chapter II of this report, the experimental study of the mechanical properties of the selected sheet steels are presented in detail. The material test results are evaluated in Chapter III. Finally, conclusions are presented in Chapter IV

Design of automotive structural components using high strength sheet steels effect of strain rate on the structural strength and crushing behavior of cold-formed steel stub columns

INTRODUCTION In the past, a considerable amount of theoretical and experimental research has been undertaken to study material properties and the behavior of structures under dynamic loads and impact loads. For the purpose of investigating the structural behavior and strength of cold-formed steel members under dynamic loads, a research project was conducted at the University of Missouri-Rolla from January 1988 through December 1991 to study the effect of strain rate on mechanical properties of sheet steels and the structural behavior and strength of cold-formed steel members. The test results of material properties, stub columns, and beams with evaluations were summarized in the Eighteenth Progress Report 1. Because the previous studies were limited only to the structural members which were assembled with the same material in a given section, the research work reported herein under the sponsorship of the American Iron and Steel Institute (AISI) was concentrated on a study of the structural strength of hybrid automotive structural components using different sheet steels. In the first phase of the project, two selected sheet steels (25AK and 50SK) have been tested for establishing the mechanical properties in tension and compression under different strain rates. The nominal yield strengths of these two sheet steels are equal to approximately 25 and 50 ksi and the range of strain rates used in the test varied from 10- 4 to 1.0 in./in./sec. Details of the tension and compression coupon tests were presented in the Seventeenth Progress Report 2. Due to the lack of drop tower test equipment at the University of Missouri-Rolla, a total of fifty-two (52) drop tower tests of stub columns were conducted at General Motors Corporation during the Summer of 1992. The impact velocities used in the drop tower tests were 28.5 and 43.2 km/hr. The research findings are presented in Reference 3. At the University of Missouri-Rolla, the study of stub columns including hybrid sections fabricated from 25AK and 50SK sheet steels subjected to dynamic loads was initiated in January 1993. Ninty-six (96) box-shaped stub columns and forty-eight (48) hat-shaped stub columns were tested under the strain rates varied from 10-4 to 10- 1 in./in./sec. The test results of a total of 144 test specimens were reported herein. Among these specimens, 80 specimens were hybrid sections. In Chapter II of this report, the literature review is related to the structural strength of steel members under dynamic loading conditions. The experimental investigation of the structural behavior of stub columns subjected to static and dynamic loads are discussed in Chapter III. The test data of specimens fabricated from two types of sheet steels are evaluated in Chapter IV. summarized in Chapter V. Finally, the results of stub column tests are summarized in Chapter V

Design of automotive structural components using high strength sheet steels structural strength of cold-formed steel members under dynamic loads

INTRODUCTION During recent years, more economic and lighter vehicles have been produced by automotive manufacturers because of the high cost of fuel. High strength sheet steels have been favorably used to accomplish the construction of such automobiles. One source of the design information for using sheet steels is provided in the AISI Automotive Steel Design Manual 1. In view of the fact that material properties and stress-strain relationships of sheet steels can be influenced by the strain rate, the material properties of three different sheet steels (35XF, 50XF, and 100XF) have been studied at University of Missouri-Rolla. This study involved primarily with the experimental determination of the mechanical properties in tension and compression under different strain rates from 10- 4 to 1.0 in./in./sec. The yield strengths of three types of sheet steels ranged from 35 to 100 ksi. The test results obtained from this study were presented in the Eleventh 2 and Twelfth 3 Progress Reports. Subsequently, the same results were used to evaluate the member strengths of stub columns and flexural members. During the period from August 1989 through April 1990, the structural behavior and strength of steel members having both unstiffened and stiffened elements were studied experimentally for stub columns and beams fabricated from 3SXF sheet steel. The test results were presented in the Thirteenth 4 and Fourteenth 5 Progress Reports. In the Thirteenth Progress Report, the w/t ratios for stub columns with the unstiffened elements ranged from 8.93 to 20.97 and the w/t ratios for stub columns with stiffened elements ranged from 26.92 to 53.39. The strain rates for stub column tests varied from 10-4 to 10- 1 in./in./sec. In order to study the behavior of cold-formed steel members with large w/t ratios, I-shaped sections having unstiffened elements with w/t ratios of about 44 and box-shaped sections having stiffened elements with w/t ratios of about 100 were fabricated from 35XF sheet steel and tested in August 1990. The test results and the evaluation are presented in Chapter II and Chapter III of this report, respectively. In addition, 48 stub columns have also been fabricated from 50XF sheet steel for static and dynamic tests. These specimens were tested during the period from August through October 1990. Because the current effective design width formulas were originally derived from the test results obtained from the static tests ,the main purpose of this study was to determine the validity of the current formulas for structural members subjected to dynamic loads. In Chapter II of this report, the experimental investigation of stub columns is discussed in detail. The test data are evaluated in Chapter III. In Chapter IV, the present and future research work are summarized and the conclusions are drawn on the basis of the available test results

Design of automotive structural components using high strength sheet steels structural strength of cold-formed steel beams under dynamic loads

INTRODUCTION It has long been recognized that material properties and stress-strain relationships of sheet steels can be influenced by the strain rate. A considerable amount of theoretical and experimental research have been undertaken in the past to study material properties and the behavior of structures under dynamic loads and impact loads. In view of the fact that in the current AISI Automotive Steel Design Manual 1, the design criteria for effective design width are based on the test results under static loading condition, the objective of this investigation was to study the validity of these effective design width formulas for the design of cold-formed steel structural members subjected to dynamic loads. In order to investigate the structural behavior and strength of cold-formed steel members under dynamic loads, the material properties of three selected sheet steels (35XF, 50XF, and 100XF) have been studied at the University of Missouri-Rolla. The test results of the static and dynamic mechanical properties in tension and compression under different strain rates were established in the first phase of the project. The nominal yield strengths of these three types of sheet steels ranged from 35 to 100 ksi and the range of strain rates varied from 10-4 to 1.0 in./in./sec .. Details of the tension and compression coupon tests were presented in the Eleventh and Twelfth Propress Reports 2,3. In Phase II of the project, the structural behavior and strength of cold-formed steel members having both unstiffened and stiffened elements were studied experimentally and analytically for stub columns and beams subjected to dynamic loads. Two materials (35XF and 50XF) were used in this phase of study. The test results of 97 stub columns with evaluation were summarized in the Fifteenth Progress Report 6. During the period from August 1989 through April 1990, fifteen (15) beam specimens using channel sections and fifteen (15) beam specimens using hat sections were tested to study the strength of structural members having unstiffened and stiffened compression elements, respectively. These test specimens were fabricated from 35XF sheet steel. The strain rates ranged from 10-5 to 10-2 in./in./sec .. The test results were presented in the Thirteenth and Fourteenth Propress Reports 4, 5. The study of beam specimens fabricated from 50XF sheet steel subjected to dynamic loads was initiated in March 1991. Fifteen (15) beam specimens using channel sections and fifteen (15) beam specimens using hat sections were tested for the purpose of studying the behavior of unstiffened and stiffened compression elements, respectively. The strain rates for these beam tests varied from 10-5 to 10-2 in./in./sec. In Chapter II, the experimental investigation of beam specimens is discussed in detail. The test data of beam specimens fabricated from two types of sheet steels (35XF and 50XF) are evaluated in Chapter III. Finally, the results of beam tests are summrized in Chaper IV

Design of automotive structural components using high strength sheet steels transformed section method for the calculation of yield moment of cold-formed steel hybrid beams

INTRODUCTION It has been recognized that material properties and stress-strain relationships of sheet steel can be influenced by the strain rate. Because the member strength is also influenced by dynamic loading, a large number of research projects were conducted for a variety of structural members under specified loading conditions during past three decades. In cold-formed steel design, local buckling is one of the major design features because of the use of large width-to-thickness ratios for compression elements. For the purpose of determining the load-carrying capacity of automotive components, the effective width approach has been used. In view of the fact that the design criteria for effective design widths included in the current AISI Automotive Steel Design Manual [1] are primarily based on the results of static tests of cold-formed steel members corresponding to a strain rate approximately 1.7x10-6 in./in./sec., an investigation was conducted at University of Missouri-Rolla (UMR) since 1989 under the sponsorship of the American Iron and Steel (AISI) to study the validity of these effective design width formulas for the design of cold-formed steel automotive components subjected to dynamic loads (Pan and Yu [2], Kassar and Yu [3]). The results presented in Reference [2] showed that the effective cross-sectional area calculated on the basis of the dynamic yield stresses can be employed in the determination of ultimate loads. Because previous research projects were limited only to the structural members which were fabricated from one material or assembled with the same material in a given section, and it is known that the application of higher strength steels to structures often results in significant material-cost savings, the study of beam specimens fabricated from two types of sheet steels subjected to dynamic loads was initiated in October 1993. In this study, a total of 72 beam specimens fabricated from two different sheet steels (25AK and 50 SK) were tested under different strain rates to study the structural strength and behavior of hybrid sections. The strain rates used in the beam tests were from 10-4 to 10-2 in./in./sec.. The test results of hybrid beam specimens were presented in the Twentieth Progress Report [4]. In 1964, Ronald Frost and Charles Schilling [5] studied the behavior of hybrid plate girders consisting of higher-strength steel flanges connected with lower-strength steel webs, under pure bending and combined shear and bending. They suggested that the maximum bending strength of a hybrid beam may be considered to be (1) the moment causing the cross section to become fully plastic or (2) the moment causing initial yielding in the flange, because it has been demonstrated that the yielding which occurs in the webs of hybrid beams has little effect on the behavior of such beams. Pan and Yu [4] concluded that the available effective design width formulas using dynamic material properties can be adequately used for the design of hybrid structural members fabricated from two different materials subjected to dynamic loads. In addition, the procedures discussed in the 20th Progress Report [4] can provide a reasonable approach for calculating the critical local buckling moment, the yield moment, and the ultimate moment. However, due to the complexity for the calculation of ultimate moment using inelastic reserve capacity and the possible excessive deflection, it is suggested that for practical design, the yield moment can be used for the load-carrying capacity of hybrid beams. In this report, an alternative computing procedure was developed and utilized in the calculation of load-carrying capacity of cold-formed steel hybrid beams. The tests of hybrid beam specimens subjected to dynamic loading conditions are discussed in Chapter 2 of this report. In Chapter 3, the alternative procedures for calculating the flexural strength of hybrid beams are presented. Finally, the research findings are summarized in Chapter 4

Design of automotive structural components using high strength sheet steels effect of strain rate on the structural strength of cold-formed steel hybrid beams

INTRODUCTION In cold-formed steel design, local buckling is one of the major design features because of the use of large width-to-thickness ratios for compression elements. For the purpose of determining the load-carrying capacity of automotive components, the effective width approach has been used. In view of the fact that the design criteria for effective design width included in the AISI Automotive Steel Design Manual 1 are based on the test results for static loading condition, an investigation was conducted at University of Missouri-Rolla from January 1988 through December 1991 to study the validity of these effective design width formulas for the design of cold-formed steel automotive components subjected to dynamic loads. The results showed that the effective cross-sectional area calculated on the basis of the dynamic yield stresses can be employed in the determination of ultimate loads. The test results of material properties, stub columns, and beams with evaluations were summarized in the Eighteenth Progress Report 2. In the previous UMR research, stub column and beam specimens fabricated from two different sheet steels (35XF and 5OXF) were tested under different strain rates to study the behavior of stiffened and unstiffened compression elements. Because the previous studies were limited only to the structural members which were assembled with the same material in a given section, this portion of the research was concentrated on a study of the structural strength of hybrid automotive structural components using different sheet steels. In the first phase of the investigation, two selected sheet steels (25AK and 5OSK) have been tested in order to study the effect of strain rate on the tensile and compressive mechanical properties. The nominal yield strengths of these two types of sheet steels were 25 and 50 ksi and the range of strain rates used in the tests varied from 10- 4 to 1.0 in. /in./sec. The test results obtained from this study were presented in the Seventeenth Progress Report 3. The structural behavior and strength of cold-formed steel stub columns assembled with these two selected sheet steels were studied experimentally and analytically under dynamic loads. In the second phase of the investigation, ninety-six (96) box-shaped stub columns and forty-eight (48) hat-shaped stub columns were tested under the strain rates varied from 10-4 to 10-1 in./in./sec. at the University of Missouri-Rolla. In addition, fifty-two (52) drop tower tests of stub columns were conducted at General Motors Corporation. Details of stub column tests with evaluations were presented in the Nineteenth Progress Report 4. The test results showed that a good prediction for the ultimate strength of hybrid stub columns can be achieved by employing the dynamic material properties in the calculation of the effective cross-sectional area. The study of beam specimens fabricated from two types of sheet steels (25AK and 50SK) subjected to dynamic loads was initiated in October 1993. A total of 72 hat-shaped beams were tested to investigate the structural behavior and strength of hybrid sections using different sheet steels. The range of strain rates used in the beam tests were from 10-4 to 10-2 in./in./sec. The test results of beam specimens are reported herein. A review of the available literature on the effect of impact loads or dynamic loads on the structural strength of beams is presented in Chapter II of this report. The experimental investigation of the structural behavior of hat-shaped beam specimens subjected to dynamic loads is discussed in Chapter III. In Chapter IV, the test data for beam specimens are evaluated and presented. Finally, the research findings are summarized in Chapter V