Quasi-Analytic Sensitivity Analysis of a Unified Viscoplastic Constitutive Model for a Solder Alloy

1997 ◽  
Vol 50 (11S) ◽  
pp. S44-S49 ◽  
Author(s):  
Martin A. Eisenberg ◽  
Erhard Krempl ◽  
Luca Maciucescu
Keyword(s):  
Sensitivity Analysis ◽  
Solder Alloy ◽  
Mechanical Response ◽  
Constitutive Models ◽  
Professional Judgment ◽  
Multidisciplinary Teams ◽  
Algebraic Equations ◽  
Linear Algebraic Equations ◽  
Engineering Alloys ◽  
High Homologous Temperature

Unified constitutive models for the consistent description of inelastic thermomechanical response of engineering alloys to widely varying control conditions are strongly nonlinear; there are numerous constants to be determined; and successful use depends critically on expert professional judgment. These circumstances are not unlike those associated with the design of complex systems dependent on successful interaction of multidisciplinary teams. Introduced in this paper is a paradigm for design of constitutive models motivated by modern system design methodologies. Specifically, a quasi-analytic sensitivity analysis is applied to a special form of a viscoplasticity-based overstress model (VBO) for the uniaxial, isothermal, high-homologous temperature mechanical response of a solder alloy. Parameter sensitivity is demonstrated via linear algebraic equations. The technique is a critical first step to application of sophisticated techniques of multidisciplinary design optimization (MDO) to constitutive modeling.

Aerodynamic Sensitivity Analysis Methods for the Compressible Euler Equations

1991 ◽  
Vol 113 (4) ◽  
pp. 681-688 ◽  
Author(s):  
Oktay Baysal ◽  
Mohamed E. Eleshaky
Keyword(s):  
Sensitivity Analysis ◽  
Euler Equations ◽  
Analytical Approach ◽  
Direct Method ◽  
Pressure Coefficient ◽  
Mathematical Formulation ◽  
Computational Time ◽  
Algebraic Equations ◽  
Sensitivity Coefficients ◽  
Linear Algebraic Equations

A mathematical formulation is developed for aerodynamic sensitivity coefficients based on a discretized form of the compressible, two-dimensional Euler equations. A brief motivating introduction to the aerodynamic sensitivity analysis and the reasons behind an integrated flow/sensitivity analysis for design algorithms are presented. Two approaches to determine the aerodynamic sensitivity coefficients, namely, the finite difference approach, and the quasi-analytical approach are discussed with regards to their relative accuracies and involved computational efforts. In the quasi-analytical approach, the direct and the adjoint variable methods are formulated and assessed. Also, several methods to solve the system of linear algebraic equations, that arises in the quasi-analytical approach, are investigated with regards to their accuracies, computational time and memory requirements. A new flow prediction concept, which is an outcome of the direct method in the quasi-analytical approach, is developed and illustrated with an example. Surface pressure coefficient distributions of a nozzle-afterbody configuration obtained from the predicted flow-field solution are compared successfully with their corresponding values obtained from a flowfield analysis code and the experimental data.

scholarly journals Development of a finite-element-based design sensitivity analysis for buckling and postbuckling of composite plates

1995 ◽  
Vol 1 (3) ◽  
pp. 255-274 ◽  
Author(s):  
Ruijiang Guo ◽  
Aditi Chattopadhyay
Keyword(s):  
Sensitivity Analysis ◽  
Finite Element ◽  
Linear Equations ◽  
Composite Plates ◽  
Material Model ◽  
Design Sensitivity ◽  
Algebraic Equations ◽  
Sensitivity Derivatives ◽  
Analysis Technique ◽  
Linear Algebraic Equations

A finite element based sensitivity analysis procedure is developed for buckling and postbuckling of composite plates. This procedure is based on the direct differentiation approach combined with the reference volume concept. Linear elastic material model and nonlinear geometric relations are used. The sensitivity analysis technique results in a set of linear algebraic equations which are easy to solve. The procedure developed provides the sensitivity derivatives directly from the current load and responses by solving the set of linear equations. Numerical results are presented and are compared with those obtained using finite difference technique. The results show good agreement except at points near critical buckling load where discontinuities occur. The procedure is very efficient computationally.

Effects of Material Properties Estimations on the Thermo-Elastic Analysis for Functionally Graded Thick Spheres and Cylinders

2007 ◽  
Author(s):  
P. Ghaderi ◽  
M. Bankehsaz
Keyword(s):  
Material Properties ◽  
Mechanical Response ◽  
Functionally Graded ◽  
Elastic Response ◽  
Algebraic Equations ◽  
Linear Algebraic Equations ◽  
Constant Coefficients ◽  
Elastic Responses ◽  
Particulate Reinforced Composites ◽  
Material Gradation

In this paper effects of material properties estimations, used for particulate reinforced composites, on the thermo-mechanical response of functionally graded sphere and cylinder are presented. A numerical solution for an arbitrary material gradation is obtained for each geometry independently. With this assumption, the governing partial differential equations are reduced to an ordinary differential equation in each geometry. The thermo-elastic solution for hollow sphere is derived using spherical symmetry. However, plane strain and axial symmetry are assumed for solving hollow cylinder. In the numerical method, radial domain is divided into some finite sub-domains and material properties are assumed to be constant in each sub-domain. With this assumption, the governing thermal and mechanical equations in each sub-domain are an ODE with constant coefficients. Imposing the continuity conditions at the interface of the adjacent sub-domains, together with the global boundary conditions, a set of linear algebraic equations are derived. Solving the linear algebraic equations, the thermo-elastic responses for the thick-walled FG sphere and cylinder are obtained. Three methods of gradation are used for comparing the effects of different material properties estimations on the results; Rule of Mixtures as a conventional method, Mori-Tanaka estimation and self-consistent scheme. The results show that estimations for material properties could be influential to the thermo-elastic response for some profiles of volume fractions of constituents. However, the effect on elastic response is negligible.

On Improved Approximate Solution of the Fredholm Integral Equation

2006 ◽  
Vol 6 (3) ◽  
pp. 264-268
Author(s):  
G. Berikelashvili ◽  
G. Karkarashvili
Keyword(s):  
Integral Equation ◽  
Approximate Solution ◽  
Fredholm Integral Equation ◽  
Algebraic Equations ◽  
Order Convergence ◽  
One Dimensional ◽  
Averaging Operator ◽  
Linear Algebraic Equations ◽  
Convergence Solution

AbstractA method of approximate solution of the linear one-dimensional Fredholm integral equation of the second kind is constructed. With the help of the Steklov averaging operator the integral equation is approximated by a system of linear algebraic equations. On the basis of the approximation used an increased order convergence solution has been obtained.

scholarly journals Exact statistical solution for the hopping transport of trapped charge via finite Markov jump processes

2021 ◽  
Vol 11 (1) ◽  
Author(s):  
Andrey A. Pil’nik ◽  
Andrey A. Chernov ◽  
Damir R. Islamov
Keyword(s):  
Charge Transport ◽  
Thin Layers ◽  
Jump Processes ◽  
Dielectric Films ◽  
Algebraic Equations ◽  
Markov Jump ◽  
Statistical Solution ◽  
Linear Algebraic Equations ◽  
Special Cases ◽  
Thin Dielectric Films

AbstractIn this study, we developed a discrete theory of the charge transport in thin dielectric films by trapped electrons or holes, that is applicable both for the case of countable and a large number of traps. It was shown that Shockley–Read–Hall-like transport equations, which describe the 1D transport through dielectric layers, might incorrectly describe the charge flow through ultra-thin layers with a countable number of traps, taking into account the injection from and extraction to electrodes (contacts). A comparison with other theoretical models shows a good agreement. The developed model can be applied to one-, two- and three-dimensional systems. The model, formulated in a system of linear algebraic equations, can be implemented in the computational code using different optimized libraries. We demonstrated that analytical solutions can be found for stationary cases for any trap distribution and for the dynamics of system evolution for special cases. These solutions can be used to test the code and for studying the charge transport properties of thin dielectric films.

scholarly journals Two matrix methods for solution of nonlinear and linear Lane-Emden type equations with mixed condition by operational matrix

2015 ◽  
Vol 4 (3) ◽  
pp. 420 ◽  
Author(s):  
Behrooz Basirat ◽  
Mohammad Amin Shahdadi
Keyword(s):  
Bernstein Polynomials ◽  
Operational Matrix ◽  
Numerical Procedure ◽  
Operational Matrices ◽  
Algebraic Equations ◽  
Mixed Condition ◽  
Matrix Methods ◽  
Numerical Examples ◽  
Linear Algebraic Equations ◽  
The Given

<p>The aim of this article is to present an efficient numerical procedure for solving Lane-Emden type equations. We present two practical matrix method for solving Lane-Emden type equations with mixed conditions by Bernstein polynomials operational matrices (BPOMs) on interval [<em>a; b</em>]. This methods transforms Lane-Emden type equations and the given conditions into matrix equation which corresponds to a system of linear algebraic equations. We also give some numerical examples to demonstrate the efficiency and validity of the operational matrices for solving Lane-Emden type equations (LEEs).</p>

scholarly journals Optimal Random Packing of Spheres and Extremal Effective Conductivity

Symmetry ◽  
2021 ◽  
Vol 13 (6) ◽  
pp. 1063
Author(s):  
Vladimir Mityushev ◽  
Zhanat Zhunussova
Keyword(s):  
Effective Conductivity ◽  
Dimensional Space ◽  
Elementary Function ◽  
Voronoi Tessellation ◽  
Random Packing ◽  
Periodicity Cell ◽  
Algebraic Equations ◽  
Optimal Packing ◽  
Linear Algebraic Equations ◽  
Initial Location

A close relation between the optimal packing of spheres in Rd and minimal energy E (effective conductivity) of composites with ideally conducting spherical inclusions is established. The location of inclusions of the optimal-design problem yields the optimal packing of inclusions. The geometrical-packing and physical-conductivity problems are stated in a periodic toroidal d-dimensional space with an arbitrarily fixed number n of nonoverlapping spheres per periodicity cell. Energy E depends on Voronoi tessellation (Delaunay graph) associated with the centers of spheres ak (k=1,2,…,n). All Delaunay graphs are divided into classes of isomorphic periodic graphs. For any fixed n, the number of such classes is finite. Energy E is estimated in the framework of structural approximations and reduced to the study of an elementary function of n variables. The minimum of E over locations of spheres is attained at the optimal packing within a fixed class of graphs. The optimal-packing location is unique within a fixed class up to translations and can be found from linear algebraic equations. Such an approach is useful for random optimal packing where an initial location of balls is randomly chosen; hence, a class of graphs is fixed and can dynamically change following prescribed packing rules. A finite algorithm for any fixed n is constructed to determine the optimal random packing of spheres in Rd.

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