Hydrostatic equilibrium

About: Hydrostatic equilibrium is a research topic. Over the lifetime, 2451 publications have been published within this topic receiving 62172 citations.

Static and free vibration analysis of gravity dam under the influence of hydrostatic pressure using ANSYS finite element models

Abstract: Abstract Dams are considered to be very important structures as they play an important role in the economic and social development of the area in which it is being constructed as well as utilized for hydropower generation. The concrete gravity dam is a solid structure that retains its stability against the design loads through its self-weight alone. The dam considered in this study is a structure of the Indirasagar polavaram gravity dam which is located in the village called Ramayyapeta comes under the West Godavari District, Andhra Pradesh. In this study, the finite element (FE) method is employed to numerically analyze the 2-D concrete gravity dam. The main objective of this study is to perform a linear FE analysis of the Indirasagar Polavaram gravity dam by varying the upstream hydrostatic pressure with constant downstream tailwater pressure. In the static analysis parameters like displacements, stresses and strains are assessed at each node, and their corresponding distributions are noticed. Subsequently, in the dynamic analysis approach, only free vibration analysis (Modal analysis) is done by considering only the dam's weight, the first five-mode shapes and their respective natural frequencies are extracted using ANSYS. The linear material behavior of the dam is modeled using the quadrilateral 4 node PLANE182 elements and the hydrostatic pressure is applied as triangular distribution. From the numerical analysis, it is concluded that the maximum tensile stresses are accumulated at the heel portion of the dam for cases 1 to 4, whereas it is observed distributed along the dam base for the rest of the cases. The lateral displacement and strain are observed maximum for case 1. The First mode's natural frequency of 5.81 Hz is ascertained and the maximum frequency and displacement are produced under the fifth mode.

Role of σR2 + γRμνTμν model on anisotropic polytropes

Abstract: This paper analyzes the anisotropic stellar evolution governed by polytropic equation-of-state in the framework of f(R,T,Q) gravity, where Q = RabTab. We construct the field equations, hydrostatic equilibrium equation and trace equation to obtain their solutions numerically under the influence of σR2 + γQ gravity model, where σ and γ are arbitrary constants. We examine the dependence of various physical characteristics such as radial/tangential pressure, energy density, anisotropic factor, total mass and surface redshift for specific values of the model parameters. The physical acceptability of the considered model is discussed by verifying the validity of energy conditions, causality condition and adiabatic index. We also study the effects arising due to strong nonminimal matter-curvature coupling on anisotropic polytropes. It is found that the polytropic stars are stable and their maximum mass point lies within the required observational Chandrasekhar limit.

Stable SIP Discontinuous Galerkin Approximations of the Hydrostatic Stokes Equations

Abstract: We propose a Discontinuous Galerkin (DG) scheme for the numerical solution of the Hydrostatic Stokes equations in Oceanography. This new scheme is based on the introduction of the symmetric interior penalty (SIP) technique for the Hydrostatic Stokes mixed variational formulation. Recent research showed that stability of the mixed formulation of Primitive Equations requires LBB (Ladyzhenskaya--Babu\v{s}ka--Brezzi) inf-sup condition and an extra hydrostatic inf-sup restriction relating the pressure and the vertical velocity. This hydrostatic inf-sup condition invalidates usual Stokes continuous finite elements like Taylor-Hood $P_2/P_1$ or bubble $P_{1,b}/P_1$. Here we consider $P_k/P_k$ discontinuous finite elements and, using adequate LBB-like and hydrostatic discrete inf-sup conditions we can demonstrate stability of the SIP DG scheme in the natural energy norm for this problem. Finally, according numerical tests are provided.

A terrain-following coordinate system—Derivation of diagnostic relationships

Abstract: Generalized hydrostatic and geostrophic equations can be derived from the equations in the terrain-following framework. The generalized hydrostatic equation permits some non-hydrostatic motions (as obtained from a Cartesian framework) to remain when a non-zero slope exists. Correspondingly, the generalized geostrophic wind permits a horizontal divergent component (in addition to divergence caused by the change of Coriolis parameter with latitude) to occur when the slope angle is not zero.

Reliability analysis of base sliding of concrete gravity dams subjected to earthquakes

Abstract: Concrete gravity dams are typically constructed in blocks separated by vertical contraction joints. The design of straight concrete gravity dams is traditionally performed by assuming each block to be independent, except for gravity dams in valleys with relatively small width to height ratios. Understanding the 2-D behaviour of individual monoliths is thus considered relevant and 2-D models are usually employed in safety evaluations of existing dams. During a strong seismic event, low to medium height concrete gravity dams tend to crack at the base as opposed to tall dams, which attract high stresses and cracking at the level of a slope change on the downstream side of a dam. The state-of-the-practice in the seismic evaluation of concrete gravity dams requires that the failure mode of the dam monolith sliding at its base be considered. This study focused on the post-crack dynamic response of existing concrete gravity dams in order to investigate their safety against sliding considering non-linear effects in the damfoundation interface. Sliding response of a single monolith of a low to medium height concrete gravity dam at the failure state was studied and, therefore, the monolith separated or unbonded from its foundation was considered. The work included experimental, analytical and reliability studies. During the experimental study, a model of an unbonded concrete gravity dam monolith was developed and tested using a shake table. The model, preloaded by a simulated hydrostatic force, was subjected to a selected variety of base excitations. Other effects, such as hydrodynamic and uplift pressures were not considered in the experiments. A strong influence of amplitude and frequency of the base motions on the sliding response of the model was observed during the tests. Simple and more detailed numerical models to simulate the experiments were developed during the analytical study. It was observed that a simple rigid model could simulate acceptably the tests only in a limited range of excitation frequencies. A finite element (FE) model simulated the experiments satisfactorily over a wider range of dominant frequencies of the base accelerations. The numerical models were used to simulate the seismic response of a 45 m high monolith of a concrete gravity dam subjected to three different earthquake excitations for varying reservoir's water level. The agreement between the results using the simple rigid and the FE models was found acceptable. The results of the numerical simulations were used in a reliability analysis to calculate probabilities of failure of the 45 m high monolith. Probability of failure was defined here as an annual chance of exceeding an allowable amount of the monolith's base sliding during an earthquake. The peak ground acceleration (PGA), the characteristics of the time history, and the reservoir's water level were considered as random parameters during this study. Using the FE model, the annual probabilities of failure ranged from 1. 1E-8 for the mean PGA of 0.2g and 20 cm of allowable sliding to 1.3E-3 for the mean PGA of 0.6g and 1 cm of allowable sliding. The probabilities of failure using the simple rigid model were found close to those using the FE model. It was concluded that the computationally less demanding simple rigid model may be adequately used in reliability calculations of low to medium height concrete gravity dam safety against base sliding.