Some variational principles for linear coupled thermoelasticity

Correct selection of similar materials is key to geomechanical model tests. According to similarity theories, a novel similar material for the fluid–solid coupling model test was developed to solve problems of low similarity and poor stability. A similar material is mixed with calcium carbonate, white cement, paraffin, quartz sand, silicone oil, talc, and iron powder. Quartz sand and talc powder are the main materials; white cement, calcium carbonate, and paraffin are glue; silicone oil and iron powder are regulators. The effects of different mixing ratios on the compressive strength, permeability coefficient, and specific gravity were studied using a single factor analysis method. The main components controlling the material properties were determined through numerous laboratory tests. The experimental results show that the new material strength is controlled by cement, paraffin, and calcium carbonate. Its permeability coefficient can be adjusted by altering the ratio of silicone oil and paraffin. Its specific gravity is mainly affected by iron powder. The new material can simulate low-strength and medium-strength rock materials with different permeabilities, and it can effectively solve the problem that mechanical properties and nonhydrophilic properties cannot be satisfied simultaneously. The material was successfully applied in geological model tests of fault water inrush.

Development and application of a new similar material for fluid–solid coupling model test

Discussion It was shown that the straightforward application of the Ritz procedure with piecewise cubic Hermitian interpolation functions in order to produce time finite element equations will result in an unstable algorithm. This is a rather disappointing result, if one refers, e.g., to the second-order static equilibrium problem of a rod for which the same interpolation model works so well. In the authors' opinion, in order to get a better understanding of this phenomenon, one must refer to the parent matrix K before the initial or the boundary conditions are imposed. The degeneracy of K represents the need of the number of the essential conditions that must be imposed in order to make the formulation well defined for the given problem. The parent matrix of Eqs. (4) and (5) is singular of degeneracy 1. This is exactly the single rigid-body motion that must be removed in order to make the formulation for the "static" rod problem well defined. However, in the dynamic problem, both the initial displacement and velocity are essential conditions that must be imposed in order to make the formulation well defined. Indeed, the parent matrix of the modified elements [Eqs. (12) and (13)] is singular of degeneracy 2 and both the initial displacement and velocity must be imposed in order to solve the equations.

A Quasivariational Principle for Fluid-Solid Interaction

Fluid–fluid and –solid interaction problems: Variational principles revisited

This paper presents a study and comparison of shape design sensitivity analysis algorithms that are based on the continuum adjoint variable method, the continuum direct differentiation method, and the finite difference method, implemented on a supermini computer with an attached array processor. The basic algorithms and their differences in evaluating shape design sensitivity coefficients are outlined. A solution method for solving a system of equations, using a general sparse storage technique, is used for numerical implementation of shape design sensitivity analysis. It is found that computing shape design sensitivity coefficients using the direct differentiation method is significantly more efficient than using the adjoint variable method or the finite difference method. A detailed performance evaluation of the methods, using an attached array processor, is presented. The performance of the attached array processor, compared to a supermini computer is shown to depend strongly on the type of computations to be carried out. When only parts of a program are running on an attached array processor, the CPU time distribution among the different subroutines of the program can change significantly, compared to using the host processor only.

A study of solution algorithms for shape design sensitivity analysis on a supermini computer with an attached array processor

Solution of nonlinear structural problems using array processors

The classical variational principles of fluid-solid interaction impose certain constraint as well as stringent interface conditions. The conditions which are often undesirable in obtaining approximate direct solutions are relaxed through Friedrichs’s transformation. Hence, the unconstrained variational principles are formulated which yield, as the Euler equations, all the fundamental equations of a viscous incompressible fluid and an anisotropic elastic solid immersed within the fluid of finite extent, and their interface continuity conditions.

Nesrin Sarigul

Papers

A Quasivariational Principle for Fluid-Solid Interaction

Solution of nonlinear structural problems using array processors

Certain Variational Principles with No Constraints for Fluid-Solid Strong Interaction