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Limit analysis of plane problems in soil mechanics
Published in G. Swoboda, Numerical Methods in Geomechanics Innsbruck 1988, 2017
When using the lower bound theorem, it is often difficult to manually construct statically admissible stress fields for practical problems involving complicated loading and complex geometry. A statically admissible stress field is one which satisfies the stress boundary conditions, equilibrium and nowhere violates the yield criterion (the stresses must lie inside or on the yield surface in stress space). An alternative method for computing lower bounds, which uses finite elements and linear programming, has been presented by Lysmer (1). This procedure uses 3-noded triangular elements with the nodal variables being the unknown stresses. Statically admissible stress discontinuities are permitted to occur at the interfaces between adjacent triangles. The finite element formulation leads to a linear programming problem where the objective function, which is to be maximised, corresponds to the collapse load and is expressed in terms of the unknown stresses. The unknowns are subject to a set of linear constraints arising from the stress boundary conditions, equilibrium and yield criterion. The computation of lower bound limit loads by finite elements and linear programming has been studied by several authors including Anderheggen and Knopfel (2) and Bottero et al (3).
Basis of geotechnical design
Published in Manuel Matos Fernandes, Analysis and design of geotechnical structures, 2020
This alternative presentation shows clearly why this approach is known in the literature as working stress design, WSD. The main idea is that the applied or service stress, S, does not exceed, in each structural member or cross section, a given admissible stress that is equal to the ratio of the yield or ultimate stress, R, by a factor, F, greater than one.
Reinforcement function
Published in Gerard P.T.M. Van Santvoort, Geosynthetics in Civil Engineering, 2017
Strength and stiffness are the two distinctive properties of soil reinforcement with geosynthetics. Changes in temperature, alteration, creep and damage may have a great influence on the admissible stress. Hence only polyester woven fabrics and polyester grids with a high E-modulus are suitable as reinforcing material.
Approximate controllability of non-autonomous second-order evolution hemivariational inequalities with nonlocal conditions
Published in Applicable Analysis, 2023
Jing Zhao, Zhenhai Liu, Yongjian Liu
Motivated by the aforementioned contributions, our purpose in this paper is to provide some suitable sufficient conditions for the existence of mild solutions and approximate controllability to the following non-autonomous second-order nonlinear evolution inclusion which is an equivalent form of a hemivariational inequality where are given points of a separable Hilbert space H, and is a closed densely defined operator. The notation stands for the generalized Clarke subdifferential (cf. [42]) of a locally Lipschitz function and . The control function and the admissible control set U is also a Hilbert space. are continuous functions from to H.
Optimal tracking control of mechatronic servo system using integral reinforcement learning
Published in International Journal of Control, 2022
Wei Chen, Jian Hu, Chenchen Xu, Haibo Zhou, Jianyong Yao, Weirong Nie
According to optimal control, this paper will find a control strategy that ensures the system states and track the given trajectory and respectively. Define and as the tracking error, they fulfil the following infinite-horizon value function: where is a set of admissible control policies (Abu-Khalaf & Lewis, 2005); is a utility function with positive constants .
Saddle-point equilibrium sequence in one class of singular infinite horizon zero-sum linear-quadratic differential games with state delays
Published in Optimization, 2019
Let, for a given the assumption A2 be valid. Then: the pair i.e. it is admissible in the CCDG;for any and any the admissible pair satisfies the following inequality: i.e. this pair is a saddle-point equilibrium in the regular CCDG;the value of the CCDG is for any and any the value of the CCDG is nonnegative.