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The “Snap back” problem of the micro‐cantilever remains one of the dominant failure mechanisms in the Micro Electro‐mechanical System (MEMS). By analyzing the Hamaker micro continuum medium and solid physics principle, the consistency model of Wigner‐Seitz (W‐S) continuum medium is presented. The gap revision coefficients of the body with the face‐centered cubic structure are derived, which include the attractive force and the repulsive one. The adhesion model of the 500 µ m X 1 µ m silicon micro‐cantilever coated by Au is established. The micro‐cantilever static relationship between the elastic force and the adhesion force is discussed. The reason of the microcantilever “snap back” problem, an instable balanced point, is discovered. Increasing the rigidity of the micro‐cantilever, a method to avoid the micro‐cantilever “snap back” to happen, is put forward, which improves MEMS structure design and enhances MEMS reliability.

The purpose of this paper is to review recent advances and current issues in the realm of sequentially linear analysis.

Sequentially linear analysis is an alternative to non‐linear finite element analysis of structures when bifurcation, snap‐back or divergence problems arise. The incremental‐iterative procedure, adopted in nonlinear finite element analysis, is replaced by a sequence of scaled linear finite element analyses with decreasing secant stiffness, corresponding to local damage increments. The focus is on reinforced concrete structures, where multiple cracks initiate and compete to survive.

Compared to nonlinear smeared crack models in incremental‐iterative settings, the sequentially linear model is shown to be robust and effective in predicting localizations, crack spacing and crack width as well as brittle shear behavior. To date, sequentially linear analysis has not been devised with a proper crack closing algorithm. Besides, of utmost importance for many practical applications, sequentially linear analysis requires an improvement of the algorithm to deal with non‐proportional loadings.

This article gives an up‐to‐date research overview on the applicability of sequentially linear analysis. For the issue of non‐proportional loading, it indicates solution directions.

A methodology for producing an elevated-temperature tension stiffening model is presented.

The energy-based stress–strain model of plain concrete developed by Bažant and Oh (1983) was extended to the elevated-temperature domain by developing an analytical formulation for the temperature-dependence of the fracture energy G_f. Then, an elevated-temperature tension stiffening model was developed based on the modification of the proposed elevated-temperature tension softening model.

The proposed tension stiffening model can be used to predict the response of composite floor slabs exposed to fire with great accuracy, provided that the global parameters TS and K_res are adequately calibrated against global structural response data.

In a finite element analysis of reinforced concrete, a tension stiffening model is required as input for concrete to account for actions such as bond slip and tension stiffening. However, an elevated-temperature tension stiffening model does not exist in the research literature. An approach for developing an elevated-temperature tension stiffening model is presented.

The purpose of this paper is to introduce a new arc-length control method for physically non-linear problems based on the rates of the internal and the dissipated energy.

In this paper, the authors derive from the second law of thermodynamics the arc-length method based on the rate of the dissipated energy and from the time derivative of the energy density the arc-length method based on the rate of the internal energy.

The method requires only two parameters and can automatically trace equilibrium paths which display multiple snap-through and/or snap-back phenomena.

A fully energy-based control procedure is developed, which facilitates switching between dissipative and non-dissipative arc-length control equations in a natural way. The method is applied to a plate with an eccentric hole using the phase field model for brittle fracture and to a perforated beam using interface elements with decohesion.

The purpose of this paper is to propose a path-finding algorithm to solve problems with an arbitrary load-displacement relationship which results from geometrical and material nonlinear models to simulate e.g. timber structures realistically.

A method using combined load and displacement control for the Newton method along with path-characterising measures and sub-incremention is introduced. A path-related stiffness measure is used to identify the situation when it is necessary to select the displacement control and chose the best degree of freedom as a parameter instead of the load factor. The nonlinearity index extracts information about the convergence behaviour during one incremental step. Together with the reduction of the load increments it avoids leaving the equilibrium path.

The method is discussed based on numerical examples with highly nonlinear behaviour. It is capable to solve systems with decreasing load capacity and snap-back effects.

The algorithm combines load and displacement control and adaptively choses the method and the corresponding degree of freedom and cares for reliable path following.

A new model for handling non‐orthogonal cracks within the smeared crack concept is described. It is based on a decomposition of the total strain increment into a concrete and into a crack strain increment. This decomposition also permits a proper combination of crack formation with other non‐linear phenomena such as plasticity and creep and with thermal effects and shrinkage. Relations are elaborated with some other crack models that are currently used for the analysis of concrete structures. The model is applied to some problems involving shear failures of reinforced concrete structures such as a moderately deep beam and an axisymmetric slab. The latter example is also of interest in that it confirms statements that ‘reduced integration’ is not reliable for problems involving crack formation and in that it supports the assertion that identifying numerical divergence with structural failure may be highly misleading.

The application of the preconditioned Lanczos method is proposed for the solution of the linearized equations resulting from a non‐linear solution routine based on Newton methods. A path‐following solution algorithm with an arc length method is employed for tracing all types of post‐critical branches of a load‐displacement curve. The proposed methodology retains all characteristics of an iterative method by avoiding the complete factorization of the current stiffness matrix. The necessary eigenvalue information is retained in the tridiagonal matrix of the Lanczos approach.

Resilience is the ability to snap back after experiencing trauma, and is increasingly important for leaders in today’s complex, global world. Resilience can be learned, which is a great news for leaders wanting to sustain through tough times. When adversity arises, resilience becomes the tool to help us grow stronger. Unfortunately, most organizations do not purposefully design themselves to foster a resilient workplace, leaving leaders to do this work on their own. By not investing in building resilience in employees, organizations are missing an important way to differentiate themselves from the competition. Workplaces that build resilience into their practices, culture, and development benefit from employees who sustain, even thrive, through complex change and market shifts.

This chapter explores how the habit of “stealing time” can build stronger, more resilient leaders, in adverse times. We will also discuss how reshaping our own mindset makes us stronger and ready to tackle daily challenges. Then we focus on spiritual, emotional, physical, and mental components of resilience. By increasing our resilience, we also gain a sense of cognitive freedom – a sense of empowered problem-solving and creativity – that can be a positive and contagious force throughout our teams and organizations. Finally, we focus on the organizational “streams” of resilience, which allow organizations to build greater resilience capacities at all levels. By using classic organizational design principles, we begin to see how we can help everyone live and work more fully and with more vigor.

Two different methods to obtain crack propagation curves are considered in this work. In an analytical approach, the adhesion between the plates is considered perfect. In such case, the interface stiffness is not taken into account and the classic beam theory is used to study the behavior of the plates during the delamination. The second approach is numerical and the bonded interface is now considered elastic. The paper aims to discuss these issues.

The propagation curves are obtained with the aid of the finite element code CAST3M by taking the structural response for a given value of initial crack length at a time.

A good fit is achieved when analytical and numerical curves are compared. Finally, mechanical tests results are presented to validate the numerical method and to identify the critical energy release rate (G_c ).

More than an easier method to obtain propagation curves, the numerical method presented in this paper is an important tool to selection of optimized test geometries.