Effect of boundary conditions on shakedown analysis of heterogeneous materials

The determination of the ultimate load-bearing capacity of structures made of elastoplastic heterogeneous materials under varying loads is of great importance for engineering analysis and design. Therefore, it is necessary to accurately predict the shakedown domains of these materials. The static shakedown theorem, also known as Melan's theorem, is a fundamental method used to predict the shakedown domains of structures and materials. Within this method, a key aspect lies in the construction and application of an appropriate self-equilibrium stress field(SSF). In the structural shakedown analysis, the SSF is typically constructed by governing equations that satisfy no external force(NEF) boundary conditions. However, we discover that directly applying these governing equations is not suitable for the shakedown analysis of heterogeneous materials. Researchers must consider the requirements imposed by the Hill-Mandel condition for boundary conditions and the physical significance of representative volume elements(RVEs). This paper addresses this issue and demonstrates that the sizes of SSFs vary under different boundary conditions, such as uniform displacement boundary conditions(DBCs), uniform traction boundary conditions(TBCs), and periodic boundary conditions(PBCs). As a result, significant discrepancies arise in the predicted shakedown domain sizes of heterogeneous materials. Built on the demonstrated relationship between SSFs under different boundary conditions, this study explores the conservative relationships among different shakedown domains, and provides proof of the relationship between the elastic limit(EL) factors and the shakedown loading factors under the loading domain of two load vertices. By utilizing numerical examples, we highlight the conservatism present in certain results reported in the existing literature. Among the investigated boundary conditions, the obtained shakedown domain is the most conservative under TBCs.Conversely, utilizing PBCs to construct an SSF for the shakedown analysis leads to less conservative lower bounds, indicating that PBCs should be employed as the preferred boundary conditions for the shakedown analysis of heterogeneous materials.

ABNORMAL GEOMAGNETIC FIELD RESPONSE AT INTRAPLATE TECTONIC BOUNDARY IN CONTINENT AND CONTINENTAL MARGIN IN SOUTHEASTERN CHINA

We used matched filter, spectrum analysis, and continuation methods of potential field for data processing and obtained the geomagnetic field distribution about the continent and continental margin in southeast China. On the basis of grid data, inversion was conducted and magnetic field distribution and magnetic structure on bedding of different depths were obtained. The new results show that: 1. The magnetic field characteristics are largely different in horizontal and vertical directions and they can be divided into zones according to the continental blocks of Yangtze, Cathaysia, Kangdian (Sichuan-Yunnan) and Qinling-Dabie. 2. The Tanlu fault extends southward along the Ganjiang fault and the Wuchuan-Sihui fault after it crossed over the Yangtze River and was offset locally in the east-west direction. The Tanlu fault finally slips into the South China Sea at Hainan Island. 3. The boundary between Yangtze and Cathaysia blocks starts from Hangzhou Bay in the east, extends along Jiangshao fault and passes through Nanchang, Changsha, and Guilin, and finally enters the sea at Qinzhou, Guangxi. 4. The distribution of buried structure zone is located at 24.5°-26° N.

EFFECTS OF BOUNDARY LAYER FRICTION AND TOPOGRAPHY ON THE INSTABILITY OF BAROCLINIC WAVES

In this paper,the simultaneous effects of boundary layer and topography on the instability of Eady wave are investigated by using a new parameterization of the vertical velocity at the top of PBL and the influences of the stratification of the PBL,roughness and the slope of terrain are shown.Furthermore,the effects of the boundary layer friction and topography on generalized Eady wave are also investigated.