Search

This paper investigates the near-field performance of chemical dissolution-front instability (CDFI) around a circular acid-injection-well in fluid-saturated porous media (FSPM) through using purely mathematical deductions. After the mathematical governing equations of the CDFI problem involving radially divergent flow are briefly described, both analytical base solutions and perturbation solutions for the considered problem are mathematically derived These analytical solutions lead to the theoretical expression of the perturbation induced dimensionless growth-rate and the following two new findings. The first new finding is that the critical Peclet number of a chemical dissolution system (CDS) associated with radially divergent flow in FSPM is not only a function of the permeability ratio between the undissolved and dissolved regions as well as the dimensionless wavenumber, but also a function of the circular chemical dissolution-front location relative to the circular acid-injection-well in FSPM. The second new finding is that as the direct result of considering a nonzero radius of the circular acid-injection-well, there exits a critical closeness number, which may be used to assess where the circular chemical dissolution-front starts becoming unstable in the CDS associated with radially divergent flow. Based on these two new findings, a theoretical criterion of two parts has been established. The first part of the established theoretical criterion answers the scientific question when a circular chemical dissolution-front can become unstable, while the second part of the established theoretical criterion answers the scientific question where a circular chemical dissolution-front can become unstable. Through applying the established theoretical criterion, a long-term existing mystery why the wormhole pattern of fractal nature and the compact pattern of fingering nature are formed at different locations away from the circular acid-injection-well circumference in fluid-saturated carbonate rocks has been successfully revealed. [ABSTRACT FROM AUTHOR]

This paper proposes a computational simulation procedure for simulating chemical dissolution-front instability problems, in which radially divergent flow is involved in fluid-saturated porous media. In the proposed computational simulation procedure, a combination of the finite element and finite difference methods is used to simulate a chemical dissolution-front instability problem involving radially divergent flow, while a new algorithm is used to apply a small perturbation to the problem. Particular attention is paid on simulating low-order modes of an unstable circular chemical dissolution-front propagating in a fluid-saturated porous medium, in which dissolvable materials only occupy a small part, so that the final porosity is remarkably smaller than unity when dissolvable materials are completely dissolved in the chemical dissolution system. To verify the proposed computational simulation procedure, analytical solutions for a benchmark chemical dissolution-front instability problem involving radially divergent flow are derived in a purely mathematical manner. The related computational simulation results have demonstrated that: (1) the proposed computational simulation procedure is correct and useful for simulating chemical dissolution-front instability problems, which are associated with both stable and unstable chemical dissolution systems involving radially divergent flow in fluid-saturated porous media; (2) the simulated shapes of the second-order, third-order and fifth-order modes associated with an unstable chemical dissolution-fronts are respectively an ellipse, a star of three angles and a star of five angles in the unstable chemical dissolution system involving radially divergent flow in the fluid-saturated porous medium; (3) although the heterogeneity of a porous medium can affect the propagation speed of a chemical dissolution-front, it does not affect the low-order mode shape in the unstable chemical dissolution system involving radially divergent flow in the fluid-saturated heterogeneous porous medium. [ABSTRACT FROM AUTHOR]

This paper deals with how to solve chemical dissolution-front instability problems, which are nonlinearly coupled by subsurface pore-fluid flow, reactive mass transport and porosity evolution processes in fluid-saturated porous media, through using two different computational schemes. In the first computational scheme, porosity, pressure of the pore-fluid and concentration of the solute are used as fundamental unknown variables to describe a chemical dissolution system, so that it can be named as the PPC scheme. In the second computational scheme, porosity, velocity of the pore-fluid and concentration of the solute are used as fundamental unknown variables to describe a chemical dissolution system, so that it can be named as the PVC scheme. Since the finite element equations of a chemical dissolution-front instability problem on the basis of using the PPC scheme is available, the main focus of this study is on deriving the finite element equations of a chemical dissolution-front instability problem on the basis of using the PVC scheme. In particular, analytical solutions for the property matrices of a four-node rectangular element have been derived and used in both the PVC scheme and the PPC scheme. Through comparing the computational simulation results obtained from using both the PPC scheme and the PVC scheme, it has demonstrated that: (1) if the chemical dissolution system is in a stable state, then the PPC scheme is superior to the PVC scheme because the PPC scheme uses less computational efforts than the PVC scheme; (2) if the chemical dissolution system is in an unstable state, then the PVC scheme is superior to the PPC scheme because the PVC scheme yields more accurate computational simulation results than the PPC scheme. [ABSTRACT FROM AUTHOR]

Chemical dissolution-front instability (CDFI) problems usually involve multiple temporal and spatial scales, as well as multiple processes. A key issue associated with solving a CDFI problem in a fluid-saturated rock is to mathematically establish a theoretical criterion, which can be used to judge the instability of a chemical dissolution-front (CDF) propagating in the fluid-saturated rock. This theoretical paper deals with how two different mathematical schemes can be used to precisely establish such a theoretical criterion in a purely mathematical manner, rather than in a numerical simulation manner. The main distinguishment between these two different mathematical schemes is that in the first mathematical scheme, a curved surface coordinate system is used, while in the second mathematical scheme, a planar surface coordinate system is employed. In particular, all the key mathematical deduction steps associated with using these two different mathematical schemes are described and discussed in great detail. The main theoretical outcomes of this study have demonstrated that (1) two different mathematical schemes under consideration can produce exactly the same theoretical criterion; (2) the main advantage of using the first mathematical scheme is that the interface conditions at the curved interface between the downstream and upstream regions can be easily described mathematically; (3) the main advantage of using the second mathematical scheme is that the first-order perturbation equations of the CDFI problem can be easily described in a purely mathematical manner. [ABSTRACT FROM AUTHOR]

This paper deals with how the purely mathematical approach can be used to solve transient-state instability problems of dissolution-timescale reactive infiltration (DTRI) in fluid-saturated porous rocks. Three key steps involved in such an approach are: (1) to mathematically derive an analytical solution (known as the base solution or conventional solution) for a quasi-steady state problem of the dissolution timescale, which is viewed as a frozen state of the original transient-state instability problem; (2) to mathematically deduce a group of first-order perturbation partial-differential equations (PDEs) for the quasi-steady state problem; (3) to mathematically derive an analytical solution (known as the perturbation solution or unconventional solution) for this group of first-order perturbation PDEs. Because of difficulty in mathematically solving a transient-state instability problem of DTRI in general cases, only a special case, in which some nonlinear coupling between governing PDEs of the problem can be decoupled, is considered to illustrate these three key steps in this study. The related theoretical results demonstrated that the transient chemical dissolution front can become unstable in the DTRI system of large Zh numbers when the long wavelength perturbations are applied to the system. This new finding may lay the theoretical foundation for developing innovative technique to exploit shale gas resources in the deep Earth. [ABSTRACT FROM AUTHOR]

This paper presents a unified theory to deal with when, why and how a sharp acidization dissolution front (ADF), which is represented by the porosity distribution curve, can take place in an acidization dissolution system composed of fluid-saturated porous rocks. The theory contains the following main points: (1) A reaction rate of infinity alone can lead to a sharp ADF of the Stefan-type in the acidization dissolution system. This sharp front is unstable when permeability in the downstream region is smaller than that in the upstream region. (2) For a finite reaction rate, when the acid dissolution capacity number approaches zero, the ADF can have a sharp profile of the Stefan-type either on a much smaller time scale or on a much larger time scale than the dissolution time scale. In the former case, the ADF may become unstable on a much larger time scale than the transport time scale, while in the latter case, it may become unstable if the growth rate of a small perturbation is greater than zero. (3) On the dissolution time scale, even if both the reaction rate is finite and the acid dissolution capacity number approaches zero, the profile of an ADF may not be sharp because it is in a transient state. In this case, not only can an ADF change its profile with time, but also its morphology can grow if the growth rate of a small perturbation is greater than zero. Due to the involvement of both the change rate and the growth rate of the ADF profile, it is necessary to conduct a transient linear stability analysis for determining whether or not a time-dependent ADF is stable in the acidization dissolution system. [ABSTRACT FROM AUTHOR]

The dynamic mechanism for destruction of the North China Craton (NCC) has been extensively discussed. Numerical simulation is used in this paper to discuss the effect of mantle upward throughflow (MUT) on the lithospheric heat flux of the NCC. Our results yield a three-stage destruction of the NCC lithosphere as a consequence of MUT variation. (1) In Late Paleozoic, the elevation of MUT, which was probably caused by southward and northward subduction of the paleo-Asian and paleo-Tethyan oceans, respectively, became a prelude to the NCC destruction. The geological consequences include a limited decrease of the lithospheric thickness, an increase of heat flux, and a gradual enhancement of the crustal activity. But the tectonic attribute of the NCC maintained a stable craton. (2) During Late Jurassic-Early Cretaceous, the initial velocity of the MUT became much faster probably in response to subduction of the Pacific Ocean; the conductive heat flux at the base of the NCC lithosphere gradually increased from west to east; and the lithospheric thickness was significantly decreased. During this stage, the heat flux distribution was characterized by zonation and partition, with nearly horizontal layering in the lithosphere and vertical layering in the underlying asthenosphere. Continuous destruction of the NCC lithosphere was associated with the intense tectono-magmatic activity. (3) From Late Cretaceous to Paleogene, the velocity of MUT became slower due to the retreat of the subducting Pacific slab; the conductive heat flux at the base of lithosphere was increased from west to east; the distribution of heat flux was no longer layered. The crust of the western NCC is relatively hotter than the mantle, so-called as a ‘hot crust but cold mantle’ structure. At the eastern NCC, the crust and the mantle characterized by a ‘cold crust but hot mantle.’ The western NCC (e.g., the Ordos Basin) had a tectonically stable crust with low thermal gradients in the lithosphere; whereas the eastern NCC was active with a hot lithosphere. The numerical results show that the MUT is the main driving force for the NCC destruction, whereas the complex interaction of surrounding plates lit a fuse for the lithospheric thinning. [ABSTRACT FROM AUTHOR]

The natural phenomenon associated with the chemical dissolution of dissolvable minerals of rocks can be employed to develop innovative technology in mining and oil extracting engineering. This paper presents a new alternative approach for theoretically dealing with chemical dissolution front (CDF) propagation in fluid-saturated carbonate rocks. Note that the CDF is represented by the porosity front in this study. In this new approach, the porosity, pore-fluid velocity and acid concentration are directly used as independent variables. To illustrate how to use the present new approach, an acidization dissolution system (ADS) consisting of carbonate rocks, which belongs to one of the many general chemical dissolution systems (CDSs), is taken as an application example. When the acid dissolution capacity (ADC) number (that is defined as the ratio of the volume of the carbonate rock dissolved by an acid to that of the acid) approaches zero, the present new approach can be used to obtain analytical solutions for the stable ADS. However, if the ADC number is a nonzero finite number, then numerical solutions can be only obtained for the ADS, especially when the ADS is in an unstable state. The related theoretical results have demonstrated that: (1) When the ADS is in a stable state and in the case of the ADC number approaching zero, the present new approach is mathematically equivalent to the previous approach, in which the porosity, pore-fluid pressure and acid concentration are used as independent variables. However, when the ADS is in an unstable state, the use of the present new approach leads to a free parameter that needs to be determined by some other ways. (2) The existence of a non-step-type dissolution front within a transient region should at least satisfy that none of the ADC number, injected acid velocity and reciprocal of the dissolution reaction rate is equal to zero in the stable ADS. [ABSTRACT FROM AUTHOR]

This paper aims to provide a brief introduction to recent advances in numerical algorithms and methods in the emerging computational geoscience filed with general simulation characteristics of modeling multiple chemical and physical processes that take place in ore-generating systems within the Earth's crust. Due to significant differences between Earth systems and engineering systems, the existing numerical algorithms and methods, which are designed for simulating realistic problems in the engineering fields, may not be straightforwardly used to simulate ore-generating problems without significant improvements. Thus, extensive and systematic studies have been conducted, in recent years, to develop new numerical algorithms and methods for simulating different aspects of ore-generating problems. Not only can the outcomes of these studies provide new simulation tools for better understanding the controlled dynamic mechanisms that take place in ore-generating systems, but also they have enriched the research contents of computational mechanics in the broad sense. [ABSTRACT FROM AUTHOR]

This paper deals with the theoretical aspects of chemical-dissolution front instability problems in two-dimensional fluid-saturated porous media including medium anisotropic effects. Since a general anisotropic medium can be described as an orthotropic medium in the corresponding principal directions, a two-dimensional orthotropic porous medium is considered to derive the analytical solution for the critical condition, which is used to judge whether or not the chemical dissolution front can become unstable during its propagation. In the case of the mineral dissolution ratio (that is defined as the ratio of the dissolved-mineral equilibrium concentration in the pore-fluid to the molar concentration of the dissolvable mineral in the solid matrix of the fluid-saturated porous medium) approaching zero, the corresponding critical condition has been mathematically derived when medium permeability anisotropic effects are considered. As a complementary tool, the computational simulation method is used to simulate the morphological evolution of chemical dissolution fronts in two-dimensional fluid-saturated porous media including medium anisotropic effects. The related theoretical and numerical results demonstrated that: (1) a decrease in the medium anisotropic permeability factor (or ratio), which is defined as the ratio of the principal permeability in the transversal direction to that in the longitudinal direction parallel to the pore-fluid inflow direction, can stabilize the chemical dissolution front so that it becomes more difficult for a planar chemical-dissolution front to evolve into different morphologies in the chemical dissolution system; (2) the medium anisotropic permeability ratio can have significant effects on the morphological evolution of the chemical dissolution front. When the Zhao number of the chemical dissolution system is greater than its critical value, the greater the medium anisotropic permeability ratio, the faster the irregular chemical-dissolution front grows. [ABSTRACT FROM AUTHOR]

This paper presents an efficient time-integration method for obtaining reliable solutions to the second-order nonlinear dynamic problems in structural engineering. This method employs both the backward-acceleration differentiation formula and the trapezoidal rule, resulting in a self-starting, single step, second-order accurate algorithm. With the same computational effort as the trapezoidal rule, the proposed method remains stable in large deformation and long time range solutions even when the trapezoidal rule fails. Meanwhile, the proposed method has the following characteristics: (1) it is applicable to linear as well as general nonlinear analyses; (2) it does not involve additional variables (e.g. Lagrange multipliers) and artificial parameters; (3) it is a single-solver algorithm at the discrete time points with symmetric effective stiffness matrix and effective load vectors; and (4) it is easy to implement in an existing computational software. Some numerical results indicate that the proposed method is a powerful tool with some notable features for practical nonlinear dynamic analyses. [ABSTRACT FROM AUTHOR]

This paper presents a numerical procedure for computational modeling of moving interfaces between fluid and porous medium domains. To avoid the direct description of the interface boundary conditions at the interface between the fluid and porous medium domains, Darcy's law is used to simulate fluid flows in both the fluid and porous medium domains. For the purpose of effectively simulating the fluid flow using Darcy's law, the artificial permeability of the fluid domain is used to establish a permeability ratio between the artificial permeability in the fluid domain and the real permeability in the porous medium domain. Using the proposed permeability ratio, the ratio of fluid pressure gradient in the porous medium domain to that in the fluid domain can be appropriately simulated. To verify the proposed numerical procedure, analytical solutions have been derived for a benchmark problem, which can be simulated using the proposed numerical procedure. Comparison of the numerical solutions with the derived analytical solutions has demonstrated the correctness and accuracy of the proposed numerical procedure. Through applying the proposed numerical procedure to several examples associated with the fluid-porous medium interface propagation problems, the related numerical solutions have demonstrated that: (1) the proposed numerical procedure is capable of simulating the morphological instability of the fluid-porous medium interface in a coupled fluid flow-chemical dissolution system when the system is in a supercritical state; and (2) the permeability ratio can have a considerable effect on the evolved morphologies of the fluid-porous medium interface in the coupled fluid flow-chemical dissolution system. [ABSTRACT FROM AUTHOR]

In dealing with chemical-dissolution-front propagation problems in fluid-saturated porous media, the chemical dissolution front represented by the porosity of the medium may have a very steep slope (i.e., a very large porosity gradient) at the dissolution front, depending on the mineral dissolution ratio that is defined as the equilibrium concentration of the dissolved minerals in the pore-fluid to the solid molar density of the dissolvable minerals in the solid matrix. When the mineral dissolution ratio approaches zero, the theoretical value of the porosity gradient tends to infinity at the chemical dissolution front. Even for a very small value of the mineral dissolution ratio, which is very common in geochemical systems, the porosity gradient can be large enough to cause the solution hard to converge when the conventional finite element method is used to solve a chemical dissolution problem in a fluid-saturated porous medium where the pore-fluid is compressible. To improve the convergent speed of solution, a porosity-gradient replacement approach, in which the term involving porosity-gradient computation is replaced by a new term consisting of pore-fluid density-gradient and pressure-gradient computation, is first proposed and then incorporated into the finite element method in this study. Through comparing the numerical results obtained from the proposed approach with the theoretical solutions for a benchmark problem, it has been demonstrated that not only can the solution divergence be avoid, but also the accurate simulation results can be obtained when the proposed porosity-gradient replacement approach is used to solve chemical-dissolution-front propagation problems in fluid-saturated porous media including pore-fluid compressibility. [ABSTRACT FROM AUTHOR]

This article deals with the theoretical aspects of chemical-dissolution front instability problems in two-dimensional fluid-saturated porous media including solute dispersion effects. Since the solute equilibrium concentration is much smaller than the molar density of the dissolvable mineral in a mineral dissolution system, a limit case, in which the ratio of the solute equilibrium concentration (in the pore fluid) to the molar density of the dissolvable mineral (in the solid matrix of the porous medium) approaches zero, is considered in the theoretical analysis. Under this assumption, the critical condition under which a planar chemical-dissolution front becomes unstable has been mathematically derived when solute dispersion effects are considered. The present theoretical results clearly demonstrated that: (1) the propagation speed of a planar chemical-dissolution front in the case of considering solute dispersion effects is the same as that when solute dispersion effects are neglected. This indicates that solute dispersion does not affect the propagation speed of the planar chemical-dissolution front in a fluid-saturated porous medium. (2) The consideration of solute dispersion can cause a significant increase in the critical Zhao number, which is used to judge whether or not a planar chemical-dissolution front may become unstable in the fluid-saturated porous medium. This means that the consideration of solute dispersion can stabilize a planar chemical-dissolution front, because an increase in the critical Zhao number reduces the likelihood of the planar chemical-dissolution front instability in a fluid-saturated porous medium. In addition, the present results can be used as benchmark solutions for verifying numerical methods employed to simulate detailed morphological evolution processes of chemical dissolution fronts in two-dimensional fluid-saturated porous media. [ABSTRACT FROM AUTHOR]

This paper deals with the computational simulation of both scalar wave and vector wave propagation problems in infinite domains. Due to its advantages in simulating complicated geometry and complex material properties, the finite element method is used to simulate the near field of a wave propagation problem involving an infinite domain. To avoid wave reflection and refraction at the common boundary between the near field and the far field of an infinite domain, we have to use some special treatments to this boundary. For a wave radiation problem, a wave absorbing boundary can be applied to the common boundary between the near field and the far field of an infinite domain, while for a wave scattering problem, the dynamic infinite element can be used to propagate the incident wave from the near field to the far field of the infinite domain. For the sake of illustrating how these two different approaches are used to simulate the effect of the far field, a mathematical expression for a wave absorbing boundary of high-order accuracy is derived from a two-dimensional scalar wave radiation problem in an infinite domain, while the detailed mathematical formulation of the dynamic infinite element is derived from a two-dimensional vector wave scattering problem in an infinite domain. Finally, the coupled method of finite elements and dynamic infinite elements is used to investigate the effects of topographical conditions on the free field motion along the surface of a canyon. [ABSTRACT FROM AUTHOR]

This paper deals with the coupled method of finite and dynamic infinite elements for simulating wave propagation in elastic and viscoelastic solids involving infinite domains. This method can be used to simultaneously simulate material complexities in the near field and the infinite extent of the far field. Based on the governing equations of wave motion in two-dimensional and three-dimensional elastic/viscoelastic solids, the mass and stiffness matrices of the dynamic infinite element have been derived. The proposed two-dimensional dynamic infinite element can be used to simulate both the P-wave and the SV-wave propagation within the element, while the proposed three-dimensional dynamic infinite element can be used to simultaneously simulate the Rayleigh wave, P-wave and S-wave propagation within the element. The related simulation results have demonstrated that the coupled method of finite and dynamic infinite elements can be accurately used to simulate, both physically and computationally, wave propagation in elastic/viscoelastic solids involving infinite domains. Thus, this method provides an advanced scientific tool for dealing with both scientific and engineering problems involving infinite domains. [ABSTRACT FROM AUTHOR]

The asthenosphere upwelled on a large scale in the western Pacific and South China Sea during the Cenozoic, which formed strong upward throughflow and caused the thermal structure to be changed obviously. The mathematical analysis has demonstrated that the upward throughflow velocity may have varied from 3×1011 to 6×1012 m/s. From the relationship between the lithospheric thickness and the conductive heat flux, the lithospheric heat flux in the western Pacific should be above 30 mW/m2, which is consistent with the observed data. The huge low-speed zone within the upper mantle of the marginal sea in the western Pacific reflects that the upper mantle melts partially, flows regionally in the regional stress field, forms the upward heat flux at its bottom, and causes the change of the lithospheric thermal structure in the region. The numerical simulation result of the expansion and evolution in the South China Sea has demonstrated that in the early expansion, the upward throughflow velocity was relatively fast, and the effect that it had on the thickness of the lithosphere was relatively great, resulting in the mid-ocean basin expanding rapidly. After the formation of the ocean basin in the South China Sea, the upward throughflow velocity decreased, but the conductive heat flux was relatively high, which is close to the actual situation. Therefore, from the heat transfer point of view, this article discusses how the upward heat flux affects the lithospheric thermal structure in the western Pacific and South China Sea. The conclusions show that the upward heat throughflow at the bottom of the lithospheric mantle resulted in the tectonic deformation at the shallow crust. The intensive uplifts and rifts at the crust led to the continent cracks and the expansion in the South China Sea. [ABSTRACT FROM AUTHOR]

This paper presents a research methodology associated with approximately a decade old computational geosciences. To demonstrate how it can be used to investigate the dynamic mechanisms of geological phenomenon, we use as an example the equal-distant distribution of gold deposits in a three-dimensional permeable fault within the Yilgarn Craton, Western Australia. The related numerical results demonstrate that: (1) convective pore-fluid flow in fluid-saturated porous media is the controlling dynamic mechanism leading to the equal-distant distribution of gold deposits along the fault; (2) the main characteristic of the new methodology is to change the traditionally used empirical, descriptive and qualitative methodology into the fundamentally scientific principles based predictive and quantitative methodology. Thus, this new methodology provides a modern scientific research tool for investigating the dynamic mechanisms associated with observed geological phenomena in nature. [ABSTRACT FROM AUTHOR]

Exact analytical solutions have been derived rigorously for the pore-fluid velocity, pore-fluid-flow focusing factor, stream function and excess pore-fluid pressure around and within a buried inclined elliptic inclusion in pore-fluid-saturated porous rocks. The geometric characteristics of the buried inclined elliptic inclusion are represented by the aspect ratio and dip angle of the inclusion, while the hydrodynamic characteristic is represented by the permeability ratio of the elliptic inclusion to its surrounding rock. Since an elliptic inclusion of any aspect ratio can be used to approximately represent geological faults and cracks, the present analytical solutions can be used to investigate the pore-fluid-flow patterns around buried faults and cracks within the crust of the Earth. Therefore, the present analytical solution not only provides a better understanding of the physics behind the pore-fluid-flow focusing problem around and within buried faults and cracks, but also provides a valuable benchmark solution for validating any numerical method in dealing with this kind of pore-fluid-flow focusing problem. The pore-fluid-flow focusing factor of a buried elliptic inclusion is demonstrated to be dependent on the aspect ratio, the permeability ratio and the dip angle. [ABSTRACT FROM AUTHOR]

In order to investigate the effect of material anisotropy on convective instability of three-dimensional fluid-saturated faults, an exact analytical solution for the critical Rayleigh number of three-dimensional convective flow has been obtained. Using this critical Rayleigh number, effects of different permeability ratios and thermal conductivity ratios on convective instability of a vertically oriented three-dimensional fault have been examined in detail. It has been recognized that (1) if the fault material is isotropic in the horizontal direction, the horizontal to vertical permeability ratio has a significant effect on the critical Rayleigh number of the three-dimensional fault system, but the horizontal to vertical thermal conductivity ratio has little influence on the convective instability of the system, and (2) if the fault material is isotropic in the fault plane, the thermal conductivity ratio of the fault normal to plane has a considerable effect on the critical Rayleigh number of the three-dimensional fault system, but the effect of the permeability ratio of the fault normal to plane on the critical Rayleigh number of three-dimensional convective flow is negligible. [ABSTRACT FROM AUTHOR]

This paper extends the evolutionary structural optimization method to the solution for maximizing the natural frequencies of bending vibration thin plates. Two kinds of constraint conditions are considered in the evolutionary structural optimization method. If the weight of a target structure is set as a constraint condition during the natural frequency optimization, the optimal structural topology can be found by removing the most ineffectively used material gradually from the initial design domain of a structure until the weight requirement is met for the target structure. However, if the specific value of a particular natural frequency is set as a constraint condition for a target structure, the optimal structural topology can be found by using a design chart. This design chart describes the evolutionary process of the structure and can be generated by the information associated with removing the most inefficiently used material gradually from the initial design domain of a structure until the minimum weight is met for maintaining the integrity of a structure. The main advantage in using the evolutionary structural optimization method lies in the fact that it is simple in concept and easy to be included into existing finite element codes. Through applying the extended evolutionary structural optimization method to the solution for the natural frequency optimization of a thin plate bending vibration problem, it has been demonstrated that the extended evolutionary structural optimization method is very useful in dealing with structural topology optimization problems. [ABSTRACT FROM AUTHOR]