Passive Regulation of Thermally Induced Axial Force and Displacement in Microbridge Structures

2017 ◽  
Vol 84 (12) ◽  
Author(s):  
Pezhman Hassanpour ◽  
Patricia M. Nieva ◽  
Amir Khajepour
Keyword(s):  
Analytical Model ◽  
Axial Force ◽  
Software Package ◽  
Coefficient Of Thermal Expansion ◽  
Thermomechanical Behavior ◽  
Design Parameters ◽  
Thermally Induced ◽  
Sensitivity Equations ◽  
Special Cases ◽  
Castigliano’S Theorem

The analytical model of a mechanism for regulating the thermally induced axial force and displacement in a fixed–fixed microbeam is presented in this article. The mechanism which consists of a set of parallel chevron beams replaces one of the fixed ends of the microbeam. The thermomechanical behavior of the system is modeled using Castigliano’s theorem. The effective coefficient of thermal expansion is used in the analytical model. The analytical model takes into account both the axial and bending deformations of the chevron beams. The model provides a closed-form equation to determine the thermally induced axial force and displacement in the microbeam. In addition, the model is used to derive the equations for the sensitivities of the microbeam’s axial force and displacement to the variations of the design parameters involved. Moreover, the model produces the stiffness of the chevron beams. The effect of the stiffness of the chevron beams on the dynamic behavior of the microbeam is discussed. The analytical model is verified by finite element modeling using a commercially available software package. Using the analytical model, two special cases are highlighted: a system with thermally insensitive axial force and a system with thermally insensitive axial displacement. The main application of the model presented in this article is in the design of sensors and resonators that require robustness against changes of temperature in the environment. The analytical model and the sensitivity equations can be easily integrated into optimization algorithms.

Development of Analytical Model of Cantilever Hook Performance

2005 ◽  
Vol 128 (2) ◽  
pp. 479-493 ◽  
Author(s):  
Gaurav Suri ◽  
Anthony F. Luscher
Keyword(s):  
Analytical Model ◽  
Axial Force ◽  
Polymeric Materials ◽  
Equation System ◽  
Contact Forces ◽  
Design Parameters ◽  
Future Research ◽  
Research Activity ◽  
Analytical Design ◽  
Input Design

With an increase in the use of polymeric materials in commercial products, snap-fits are attracting increased attention as alternatives to other, more traditional, joining methods. The field of snap-fit design is receiving greater attention as an engineering and research activity. Research in this area has focused on the development of performance models for individual features and heuristics for the design of snap-fit assemblies. An improved analytical model for cantilever hook snap-fit features is developed in this study. The modeling approach is a significant improvement over currently available analytical design equations. The model captures the effect of a snap-fit’s catch in causing contact forces to be offset from the beam’s neutral axis. Beam rotation, influence of axial force, and moment components on beam deformation are also incorporated by formulating a set of equations that model the system in its deformed configuration. The equation system is iteratively solved for several such configurations to model insertion and retention processes for snap-fits. The axial force component, which has been hitherto ignored in analytical design equations, is found to have significant effect on predicted snap-fit performance. The design space of cantilever hook features is explored by varying input design parameters. The model shows excellent agreement with experimental results, especially for low and medium retention angle snap-fit features. However, for high retention angle snap-fits, more accurate governing equations are required. Suggestions for possible improvements and future research directions are provided.

scholarly journals Reliability Evaluation of Fan-Out Type 3D Packaging-On-Packaging

Micromachines ◽  
2021 ◽  
Vol 12 (3) ◽  
pp. 295
Author(s):  
Pao-Hsiung Wang ◽  
Yu-Wei Huang ◽  
Kuo-Ning Chiang
Keyword(s):  
Finite Element ◽  
Thermal Cycling ◽  
Glass Substrate ◽  
High Speed ◽  
Coefficient Of Thermal Expansion ◽  
Three Dimensional ◽  
Design Parameters ◽  
Time To Failure ◽  
Wafer Level ◽  
Fine Pitch

The development of fan-out packaging technology for fine-pitch and high-pin-count applications is a hot topic in semiconductor research. To reduce the package footprint and improve system performance, many applications have adopted packaging-on-packaging (PoP) architecture. Given its inherent characteristics, glass is a good material for high-speed transmission applications. Therefore, this study proposes a fan-out wafer-level packaging (FO-WLP) with glass substrate-type PoP. The reliability life of the proposed FO-WLP was evaluated under thermal cycling conditions through finite element simulations and empirical calculations. Considering the simulation processing time and consistency with the experimentally obtained mean time to failure (MTTF) of the packaging, both two- and three-dimensional finite element models were developed with appropriate mechanical theories, and were verified to have similar MTTFs. Next, the FO-WLP structure was optimized by simulating various design parameters. The coefficient of thermal expansion of the glass substrate exerted the strongest effect on the reliability life under thermal cycling loading. In addition, the upper and lower pad thicknesses and the buffer layer thickness significantly affected the reliability life of both the FO-WLP and the FO-WLP-type PoP.

scholarly journals Impact of Cross-Tie Properties on the Modal Behavior of Cable Networks on Cable-Stayed Bridges

2015 ◽  
Vol 2015 ◽  
pp. 1-14 ◽  
Author(s):  
Javaid Ahmad ◽  
Shaohong Cheng ◽  
Faouzi Ghrib
Keyword(s):  
Analytical Model ◽  
Design Parameters ◽  
Reference Base ◽  
Cable Network ◽  
Cable Networks ◽  
Modal Behavior ◽  
Stiffness And Damping ◽  
Main Cables ◽  
The Impact ◽  
Selection Of

Dynamic behaviour of cable networks is highly dependent on the installation location, stiffness, and damping of cross-ties. Thus, these are the important design parameters for a cable network. While the effects of the former two on the network response have been investigated to some extent in the past, the impact of cross-tie damping has rarely been addressed. To comprehend our knowledge of mechanics associated with cable networks, in the current study, an analytical model of a cable network will be proposed by taking into account both cross-tie stiffness and damping. In addition, the damping property of main cables in the network will also be considered in the formulation. This would allow exploring not only the effectiveness of a cross-tie design on enhancing the in-plane stiffness of a constituted cable network, but also its energy dissipation capacity. The proposed analytical model will be applied to networks with different configurations. The influence of cross-tie stiffness and damping on the modal response of various types of networks will be investigated by using the corresponding undamped rigid cross-tie network as a reference base. Results will provide valuable information on the selection of cross-tie properties to achieve more effective cable vibration control.

scholarly journals Multi-stable composite twisting structure for morphing applications

2012 ◽  
Vol 468 (2141) ◽  
pp. 1230-1251 ◽  
Author(s):  
X. Lachenal ◽  
P. M. Weaver ◽  
S. Daynes
Keyword(s):  
Analytical Model ◽  
Material Properties ◽  
Degrees Of Freedom ◽  
Design Parameters ◽  
Engineering Structures ◽  
The Past ◽  
Wide Range ◽  
Morphing Structure ◽  
Low Mass ◽  
Unstable States

Conventional shape-changing engineering structures use discrete parts articulated around a number of linkages. Each part carries the loads, and the articulations provide the degrees of freedom of the system, leading to heavy and complex mechanisms. Consequently, there has been increased interest in morphing structures over the past decade owing to their potential to combine the conflicting requirements of strength, flexibility and low mass. This article presents a novel type of morphing structure capable of large deformations, simply consisting of two pre-stressed flanges joined to introduce two stable configurations. The bistability is analysed through a simple analytical model, predicting the positions of the stable and unstable states for different design parameters and material properties. Good correlation is found between experimental results, finite-element modelling and predictions from the analytical model for one particular example. A wide range of design parameters and material properties is also analytically investigated, yielding a remarkable structure with zero stiffness along the twisting axis.

Application of an Epoxy Cap in a Flip-Chip Package Design

1989 ◽  
Vol 111 (1) ◽  
pp. 16-20 ◽  
Author(s):  
E. Suhir
Keyword(s):  
Thermal Expansion ◽  
Flip Chip ◽  
Coefficient Of Thermal Expansion ◽  
Preliminary Test ◽  
Elastic Stability ◽  
Thermally Induced ◽  
Package Design ◽  
Silicone Gels ◽  
Low Modulus ◽  
Supporting Frame

In order to combine the merits of epoxies, which provide good environmental and mechanical protection, and the merits of silicone gels, resulting in low stresses, one can use an encapsulation version, where a low modulus gel is utilized as a major encapsulant, while epoxy is applied as a protecting cap. Such an encapsulation version is currently under consideration, parallel with a metal cap version, for the Advanced VLSI package design which is being developed at AT&T Bell Laboratories. We recommend that the coefficient of thermal expansion for the epoxy be somewhat smaller than the coefficient of thermal expansion for the supporting frame. In this case the thermally induced displacements would result in a desirable tightness in the cap/frame interface. This paper is aimed at the assessment of stresses, which could arise in the supporting frame and in the epoxy cap at low temperatures. Also, the elastic stability of the cap, subjected to compression, is evaluated. The calculations were executed for the Advanced VLSI package design and for a Solder Test Vehicle (STV), which is currently used to obtain preliminary information regarding the performance of the candidate encapsulants. It is concluded that in order to avoid buckling of the cap, the latter should not be thinner than 15 mils (0.40 mm) in the case of VLSI package design and than 17.5 mils (0.45 mm) in the case of STV. At the same time, the thickness of the cap should not be greater than necessary, both for smaller stresses in the cap and for sufficient undercap space, required for wirebond encapsulation. The obtained formulas enable one to evaluate the actual and the buckling stresses. Preliminary test data, obtained by using STV samples, confirmed the feasibility of the application of an epoxy cap in a flip-chip package design.

Thermomechanical Design for Fine Pitch 3D-IC Packages

2012 ◽  
Vol 2012 (1) ◽  
pp. 001001-001009 ◽  
Author(s):  
Akihiro Horibe ◽  
Sayuri Kohara ◽  
Kuniaki Sueoka ◽  
Keiji Matsumoto ◽  
Yasumitsu Orii ◽  
...  
Keyword(s):  
Coefficient Of Thermal Expansion ◽  
Low Cost ◽  
High Stress ◽  
High Viscosity ◽  
Thermomechanical Properties ◽  
Design Parameters ◽  
Element Analysis ◽  
Package Design ◽  
Fine Pitch ◽  
Silicon Vias

Low stress package design is one of the greatest challenges for the realization of reliable 3D integrated devices, since they are composed of elements susceptible to failures under high stress such as thin dies, metal through silicon vias (TSVs), and fine pitch interconnections. In variety of package components, an organic interposer is a key to obtain low cost modules with high density I/Os. However, the large mismatch in coefficient of thermal expansion (CTE) between silicon dies and organic laminates causes high stress in an organic package. The major parametric components in 3D devices are dies with /without Cu-TSVs, laminates, bumps, and underfill layers. Especially, the die thicknesses and underfill properties are ones of the parameters that give us some range to control as package design parameters. In general, the underfill material with a high modulus and a low CTE is effective in reducing the stress in solder interconnections between the Si die and the laminate. However, the filler content of underfill materials with such mechanical properties generally results in high viscosity. The use of high viscous materials in between silicon dies in 3D modules can degrade process ability in 3D integration. In this study, we show that the interchip underfills in 3D modules have a wider mechanical property window than in 2D modules even with fine pitch interconnections consisting mostly of intermetallic compounds (IMCs). Also the finite element analysis results show that the optimization of the structural or thermomechanical properties of organic laminates and interchip underfill contributes to reduction of stressing thinned silicon dies which may have some risks to the device performance.

scholarly journals Extension of Castigliano’s method for isotropic beams

2020 ◽  
Vol 231 (11) ◽  
pp. 4621-4640
Author(s):  
Juergen Schoeftner
Keyword(s):  
Shear Force ◽  
Strain Energy ◽  
Axial Stress ◽  
Bending Moment ◽  
Axial Direction ◽  
Present Contribution ◽  
Special Cases ◽  
Dummy Load ◽  
Complementary Strain ◽  
Castigliano’S Theorem

Abstract In the present contribution Castigliano’s theorem is extended to find more accurate results for the deflection curves of beam-type structures. The notion extension in the context of the second Castigliano’s theorem means that all stress components are included for the computation of the complementary strain energy, and not only the dominant axial stress and the shear stress. The derivation shows that the partial derivative of the complementary strain energy with respect to a scalar dummy parameter is equal to the displacement field multiplied by the normalized traction vector caused by the dummy load distribution. Knowing the Airy stress function of an isotropic beam as a function of the bending moment, the normal force, the shear force and the axial and vertical load distributions, higher-order formulae for the deflection curves and the cross section rotation are obtained. The analytical results for statically determinate and indeterminate beams for various load cases are validated by analytical and finite element results. Furthermore, the results of the extended Castigliano theory (ECT) are compared to Bernoulli–Euler and Timoshenko results, which are special cases of ECT, if only the energies caused by the bending moment and the shear force are considered. It is shown that lower-order terms for the vertical deflection exist that yield more accurate results than the Timoshenko theory. Additionally, it is shown that a distributed load is responsible for shrinking or elongation in the axial direction.

Numerical Investigation of the Effect of Balancing-Hole on the Axial Force of a Partial Emission Pump

2014 ◽  
Author(s):  
Zhang Lisheng ◽  
Jiang Jin ◽  
Xiao Zhihuai ◽  
Li Yanhui
Keyword(s):  
Axial Force ◽  
Stokes Equations ◽  
Dominant Role ◽  
Three Dimensional ◽  
Navier Stokes ◽  
Design Parameters ◽  
Navier Stokes Equations ◽  
Computational Fluid Dynamics Cfd ◽  
The Cost

In this paper numerical simulations were conducted to analyze the effects of design parameters and distribution of balancing-hole on the axial-force of a partial emission pump. The studied pump is a single stage pump with a Barske style impeller. Based on the original impeller, we designed 7 pumps with different balancing-hole diameters and the partial emission pump equipped with different impellers were simulated employing the commercial computational fluid dynamics (CFD) software Fluent 12.1 to solve the Navier-Stokes equations for three-dimensional steady flow. A sensitivity analysis of the numerical model was performed with the purpose of balancing the contradiction of numerical accuracy and the cost of calculation. The results showed that, with increasing of the capacity, the axial force varies little. The diameter of the inner balancing-hole plays a dominant role of reducing axial-force of partial emission pump, the axial-force decreases with increasing of inner balancing-hole diameter on the whole range of operation, the axial-force of impeller without inner balancing-hole is approximately 3 times larger than that of impeller with inner balancing-hole. While the diameter of outer balancing-hole has a reverse effects compared with that of inner balancing-hole. With increasing of outer balancing-hole, the axial force increases accordingly.

A new analytical model for reliability analysis of a launch vehicle system with limited test data

2018 ◽  
Vol 233 (9) ◽  
pp. 3482-3495
Author(s):  
V Murugesan ◽  
Sreejith Plappillimadam ◽  
VJ Saji ◽  
SS Maruthi ◽  
AK Anilkumar
Keyword(s):  
Reliability Analysis ◽  
Analytical Model ◽  
Test Data ◽  
Weighting Factor ◽  
Design Parameters ◽  
Launch Vehicles ◽  
Minimum Number ◽  
First Time ◽  
Propellant Rocket

Reliability is one of the critical design parameters for the launch vehicles and its systems. When the systems are ready to fly the first time, only limited test data are available and accordingly reliability assessed will be very low. However, in most cases, the new systems are derived and developed using the knowledge and experience gained from the heritage systems to meet the fresh challenges. Hence, the reliability assessed with the minimum number of tests done on the new system does not truly reflect the inherent reliability of the system. In this paper, an approach and a new analytical model are developed for the reliability assessment of systems with limited test data, giving an accurate weighting for the tests and flight experiences with similar systems. The method gives a systematic procedure for arriving at the weighting factor for test data of the pedigree system, with due consideration of the similarities between the systems and various factors influencing system reliability. The method is illustrated with a case study of a newly developed liquid propellant rocket system. The model is validated using the available test and flight data of two propulsion systems with adequate flight experience. The analytical model is generic in nature and can be applied to reliability analysis of any system, which has considerable similarities with a pedigree system.

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