Transient thermoelasticity and other body force effects in boundary element shape sensitivity analysis

In this paper, a technique to determine effectively an optimum shape of two-dimensional and axisymmetric bodies under body force is proposed. This technique is based on the iteration of a sequential search method consisting of the following steps. In the first step, the superiority or inferiority of a given shape, which satisfies the constrained conditions of design, is judged by the deviation from the design object stress value. In the second step, this given shape is modified to an optimum shape by the proportional transformation method of the finite elements, which is considered an effect of body force. By using this technique the optimum shapes of the basic problems under gravity load or centrifugal force are obtained and the results are compared with the corresponding shapes given by elementary theory. Moreover and optimum shape of the rotating disk with a rim and a bored hole is obtained by applying the optimization technique. The validity of this shape is examined experimentally by comparing with the fracture strength of a bored, uniform thickness disk.

Design Sensitivity Analysis (DSA) is a procedure for obtaining derivatives of design objectives, such as mass and strength with respect to some design parameters, such as size and shape. In the DSA methodology, we take an existing technique for computing objectives from parameters and systematically differentiate it so that the derivatives of the objectives can be computed directly, rather than employing some sort of differencing scheme to approximate derivatives. In this paper, we apply this technique to a non-linear finite element program, Radioss, and begin looking at the properties of the DSA methodology for crashworthiness simulations. It is shown that some major computational advantages can be gained by employing DSA for these kinds of problems. Besides cost savings, there are many cases where numerical differentiation results in erroneous derivatives due to numerical noise in crash simulations. It is shown that the DSA method avoids these difficulties, thus, making it quite important for use in support of design activities.

The aim of this paper is to improve the shape of specimens for biaxial experiments with respect to optimal stress states, characterized by the stress triaxiality. Gradient-based optimization strategies are used to achieve this goal. Thus, it is crucial to know how the stress state changes if the geometric shape of the specimen is varied. The design sensitivity analysis (DSA) of the stress triaxiality is performed using a variational approach based on an enhanced kinematic concept that offers a rigorous separation of structural and physical quantities. In the present case of elastoplastic material behavior, the deformation history has to be taken into account for the structural analysis as well as for the determination of response sensitivities. The presented method is flexible in terms of the choice of design variables. In a first step, the approach is used to identify material parameters. Thus, material parameters are chosen as design variables. Subsequently, the design parameters are chosen as geometric quantities so as to optimize the specimen shape with the aim to obtain a preferably homogeneous stress triaxiality distribution in the relevant cross section of the specimen.

Metal-Ceramic Functionally Graded Materials (FGM) find extensive applications in nuclear power generators, spacecraft systems, and energy conversion systems. This study aims to investigate the behavior of FGMs under transient thermal loads and time-dependent mechanical loads through finite element modeling. A 2D model is developed using COMSOL Multiphysics to simulate the behavior of a metal-ceramic FGM thick cylinder. The model considers Titanium-Zirconium-Molybdenum (TZM) alloy for metals and Silicon carbide (SiC) for ceramic. It accounts for the effects of transient thermal loads and internal time-dependent pressure exerted on the cylinder's inner surface. Thermo-mechanical properties, assumed to follow an exponential function, are incorporated into the model. Numerical analysis results are compared with established analytical solutions to validate the model. Graphical comparisons between numerical and analytical results demonstrate significant agreement, confirming the reliability of the numerical approach. This study provides insights into the behavior of metal-ceramic FGMs under transient thermal and mechanical loads. The findings underscore the effectiveness of finite element modeling in understanding complex interactions within FGMs. Future research directions include exploring more complex geometrical models, incorporating additional loading scenarios, and performing experimental validation to enhance understanding of FGM performance in real-world conditions.

The one- and two-dimensional inviscid Euler equations are formulated in an integro-differential form for shape design sensitivity analysis and optimization. The principal tool employed to derive the performance derivative sensitivity equations is the variational method, which is a continuous alternative to the discrete sensitivity analysis. Along with the sensitivity equations, the co-state equations and their boundary conditions are derived. Thereafter, based on the modal analysis of Von Neumann theory, the stability limits of the co-state equations are investigated. The stability characteristics of the co-state equations are compared with those of the Euler equations. Finally, using the criteria from the stability analysis of the state and co-state equations, some results of shape design optimization and sensitivity analysis for both quasi one- and two-dimensional Euler equations are presented. Copyright © 1999 John Wiley & Sons, Ltd.

Explicit and implicit methods for design sensitivity analysis of nonlinear structures subjected to transient dynamic loads are described. The direct differentiation method is used to calculate the sensitivities. Elastic and elasto-plastic problems undergoing large deformation are treated in the formulation. The explicit method is quite straightforward to implement for analysis as well as design sensitivity analysis: knowing all the quantities at time t, one updates the quantities for the next time point without solution of any linear system of equations, or any iterations. For the implicit method, the effective stiffness matrix for the sensitivity equation is different from that for the analysis phase due to inclusion of large deformation in the formulation. A numerical procedure to integrate the equation is proposed which uses the symmetric effective stiffness matrix from the analysis phase. Although the sensitivity analysis problem is linear, the procedure requires iterations for sensitivity calculations at each time step, as for the analysis phase. The implicit method is implemented using the pre-conditioned conjugate gradient iterative solution scheme. Numerical results for sensitivities indicate the implicit method to be more accurate than the explicit method for transient elastoplastic problems. However, the explicit method is substantially more efficient than the implicit method.

Sensitivity analysis of eigenmodes and dynamic responses for intelligent structures

Support structure and optical alignment technology of large-aperture secondary mirror measured by back transmission method

In this paper, continuum-based sizing and configuration design sensitivity analysis (DSA) and optimization methods using the established transient dynamic analysis code DYNA3D are developed. For transient dynamic analysis, the explicit central difference method is used. For the structural domain, the updated Lagrangian formulation is used since it is appropriate for the path dependent problem. The first-order variations of the kinetic energy form, strain energy form, load form, and kinematic and structural responses with respect to the sizing and configuration design variables are derived. For the updated Lagrangian formulation, the design velocity field that defines the mapping between the initial and perturbed designs is updated at each updated configuration. The direct differentiation method is used in this paper for DSA. Numerical implementation of sizing DSA, configuration DSA, and optimization of a vehicle frame and A-pillar models has been carried out using the nonlinear finite element analysis (FEA) code DYNA3D.

The shapes of waveguide structures are optimized for the uniform electromagnetic field illumination. The vector finite element method is used as an analysis method. As the design algorithm, we employ the shape optimization with a design sensitivity analysis. Performance measure function representing the field uniformity is defined in this paper and used for the calculation of the design sensitivity. The design procedure is applied to the H-plane shape optimization in the rectangular cavity structure with a rectangular waveguide feeder and the E-plane shape optimization in the two plates waveguide.

Accuracy enhancement of fatigue damage counting using design sensitivity analysis

Three methods for design sensitivity such as numerical differentiation, analytical method and semianalytical method have been developed for the last three decades. Although analytical design sensitivity analysis is exact, it is hard to implement for practical design problems. Therefore, numerical method such as finite difference method is widely used to simply obtain the design sensitivity in most cases. The numerical differentiation is sufficiently accurate and reliable for most linear problems. However, it turns out that the numerical differentiation is inefficient and inaccurate because its computational cost depends on the number of design variables and large numerical errors can be included especially in nonlinear design sensitivity analysis. Thus semi-analytical method is more suitable for complicated design problems. Moreover semianalytical method is easy to be performed in design procedure, which can be coupled with an analysis solver such as commercial finite element package. In this paper, implementation procedure for the semi-analytical design sensitivity analysis outside of the commercial finite element package is studied and computational technique is proposed, which evaluates the pseudo-load for design sensitivity analysis easily by using the design variation of corresponding internal nodal forces. Errors in semi-analytical design sensitivity analysis are examined and numerical examples are illustrated to confirm the reduction of numerical error considerably.

PurposeThe present findings report a significant influence of disc profile and thickness on the order of excitation leading to critical speed condition. Certain transverse modes of vibration of the disc have been obtained to be more susceptible to get excited while recording the lowest critical speeds.Design/methodology/approachNumerical simulation using finite-element method has been adopted due to the complicated geometry, complex loadings and intricate analytical formulation. A comprehensive analysis of exclusive as well as combination of thermal and centrifugal loads has been taken up to determine the intensity and characteristics of the individual/combined effects.FindingsThe typical gas turbine disc profile has been analyzed to predict the critical speed under the factual working condition of an aero-engine. FEM analysis of uniform and variable thickness discs have been carried out under stationary, rotating and rotating-thermal considerations while emphasizing the effect of disc profile and thickness. Centrifugal stresses developed due to rotational effect result in unceasing stiffening of the discs with higher stiffening for a greater number of nodal diameters. On the other hand, a role reversal of thermal effect from stiffening to softening is figured out with increasing numbers of nodal diameters. However, the discs are subjected to an overall stiffening effect on account of the combined centrifugal and thermal loading, with the effect decreasing with an increase in disc thickness. Under the combined loading, the order of excitation leading to critical speed condition is dependent on disc profile and thickness. Moreover, the vibrational modes (0,1) and (0,2) are identified as more prominent adverse modes corresponding to lowest critical speeds.Practical implicationsThe present findings are expected to serve as guidelines during the design phase of gas turbine discs of aeroengine applications.Originality/valueThe present work deliberates on the simulation and analysis of gas turbine disc specific to aeroengine application. The real-life disc geometry has been analyzed with due consideration of major factual operating conditions to identify the critical speed. The identification of various critical speed using numerical analysis can help to reduce the number of experimental tests required for certification.

A special boundary integral formulation had been proposed to analyse many engineering problems of conduction heat transfer in complex three-dimensional geometries (closely spaced surface and circular hole in infinite domain or simple modification of it) by Rezayat and Burton. One example of such geometries is the mold sets in the injection molding process. In this paper, an efficient and accurate approach for the design sensitivity analysis (DSA) is presented for these kinds of problems in the similar complex geometries using the direct differentiation approach (DDA) based on the above special boundary integral formulation. The present approach utilizes the implicit differentiation of the boundary integral equations with respect to the design variables (radii and locations of circular holes) to yield the sensitivity equations. A sample problem (heat transfer of injection molding cooling system) is solved to demonstrate the accuracy of the present sensitivity analysis formulation. Although the techniques introduced here are applied to a particular problem in heat transfer of injection molding cooling system, their potential application is quite broad.

Design sensitivity analysis for parameters affecting geometry, elastic–viscoplastic material constant and boundary condition by consistent tangent operator-based boundary element method