Yangjun Luo

A variable-width harmonic probe for multifrequency atomic force microscopy

In multifrequency atomic force microscopy (AFM) to simultaneously measure topography and material properties of specimens, it is highly desirable that the higher order resonance frequencies of the cantilever probe are assigned to be integer harmonics of the excitation frequency. The harmonic resonances are essential for significant enhancement of the probes response at the specified harmonic frequencies. In this letter, a structural optimization technique is employed to design cantilever probes so that the ratios between one or more higher order resonance frequencies and the fundamental natural frequency are ensured to be equal to specified integers and, in the meantime, that the fundamental natural frequency is maximized. Width profile of the cantilever probe is the design variable in optimization. Thereafter, the probes were prepared by modifying a commercial probe through the focused ion beam (FIB) milling. The resonance frequencies of the FIB fabricated probes were measured with an AFM. Results of th...

Maximal Stiffness Design of Two-Material Structures by Topology Optimization with Nonprobabilistic Reliability

Basedon the multi-ellipsoid convex modelandthe quantified measure of the nonprobabilistic reliability, topology optimization of two-material structures in the presence of parameter uncertainties is investigated. The task of the optimal design problem is to distribute a given amount of two candidate materials into the design domain for acquiring the maximal stiffness while satisfying the reliability requirement. The extended power-law interpolation scheme for material properties is employed for relaxing the two-material topological design problem into a continuous-valued optimization problem. In addition, through transforming the minimax-type optimization problemintoaseriesofdeterministiconesbyusingasequentialapproximateprogrammingstrategy,thispaperaims tomaketheoptimizationdesignnumericallytractable.Theresultingmathematicalprogrammingproblemsarethen efficientlysolvedbytheassociationofthemethodofmovingasymptoteswithaheuristiciterativemanner.Numerical investigations reveal that system uncertainties may have considerable effects on the optimal material layout of twomaterial structures. The proposed topology optimization methodology could yield a more reasonable two-material structuraldesignthan theconventional deterministic counterpart whenthe samereliabilityrequirements need tobe achieved.

Design of Large-Displacement Compliant Mechanisms by Topology Optimization Incorporating Modified Additive Hyperelasticity Technique

This paper is focused on the topology design of compliant mechanisms undergoing large displacement (over 20% of the structural dimension). Based on the artificial spring model and the geometrically nonlinear finite element analysis, the optimization problem is formulated so as to maximize the output displacement under a given material volume constraint. A modified additive hyperelasticity technique is proposed to circumvent numerical instabilities that occurred in the low-density or intermediate-density elements during the optimization process. Compared to the previous method, the modified technique is very effective and can provide more accurate response analysis for the large-displacement compliant mechanism. The whole optimization process is carried out by the gradient-based mathematical programming method. Numerical examples of a force-inverting mechanism and a microgripping mechanism are presented. The obtained optimal solutions verify the applicability of the proposed numerical techniques and show the necessity of considering large displacement in the design problem.

Sensitivity analysis of viscoplastic deformation process with application to metal preform design optimization

The sensitivity analysis of rigid viscoplastic deformation processes with application to metal preform design optimization is investigated. For viscoplastic constitutive models, the deformation process is path-dependent in nature and thus the sensitivity analysis of the deformation history is formulated in an incremental procedure. To this end, an algorithm is derived on the basis of the time integration scheme used in the primary finite element analysis, where the contact conditions are treated with the penalty method. The discretized equilibrium equations, as well as the time integration equations, are directly differentiated with respect to the design variables. The discrete form of the sensitivity equations is then solved with procedures similar to those used in the direct analysis, where the secant matrix decomposed in the direct analysis can also be utilized at each time instant. Thus the sensitivity of the deformation history is evaluated in a step-wise procedure. The present algorithm can be employed for the optimization of metal forming processes. The accuracy of the proposed sensitivity analysis as well as its applicability are demonstrated by numerical examples with reference to preform design optimization problems, where the aggregate function method is employed for converting the non-smooth Min–max type objective function into a numerically tractable one.

Optimal design of a tapping-mode atomic force microscopy cantilever probe with resonance harmonics assignment

ABSTRACT In tapping-mode atomic force microscopy, the higher harmonics generated in the tapping process provide evidence for material composition imaging based on material property information (e.g. elasticity). But problems of low amplitude and rapid decay of higher harmonics restrict their sensitivity and accessibility. The probe’s characteristic of assigning resonance frequencies to integer harmonics results in a remarkable improvement of detection sensitivity at specific harmonic frequencies. In this article, a systematic structural optimization framework is demonstrated for designing a three-layer probe with specified ratios between eigenfrequencies. An original regular cantilever probe is divided into three layers, from which the cross-sectional width of the symmetrical top and bottom layers is the design variable, while the middle layer is unchanged. Optimization constraints are the integer ratios between eigenfrequencies, and the objective is to maximize the first eigenfrequency. Numerical examples with single- and multiple-frequency constraints are investigated, which enhance significantly the frequency response at specific harmonic positions.

Stress-based topology optimization of concrete structures with prestressing reinforcements

Following the extended two-material density penalization scheme, a stress-based topology optimization method for the layout design of prestressed concrete structures is proposed. The Drucker–Prager yield criterion is used to predict the asymmetrical strength failure of concrete. The prestress is considered by making a reasonable assumption on the prestressing orientation in each element and adding an additional load vector to the structural equilibrium function. The proposed optimization model is thus formulated as to minimize the reinforcement material volume under Drucker–Prager yield constraints on elemental concrete local stresses. In order to give a reasonable definition of concrete local stress and prevent the stress singularity phenomenon, the local stress interpolation function and the ϵ -relaxation technique are adopted. The topology optimization problem is solved using the method of moving asymptotes combined with an active set strategy. Numerical examples are given to show the efficiency of the proposed optimization method in the layout design of prestressed concrete structures.

Nonlinear numerical simulation of bonded steel-concrete composite beams by finite element analysis

The steel-concrete composite beam bonded by adhesive has its particular advantages over the traditional composite beam. Based on the experimental observation of push-out test, the shear connection behaviour of concrete-adhesive interface is modelled by nonlinear springs, whereas the steel-adhesive interface is assumed connected perfectly. Then a three-dimensional nonlinear finite element model for mechanical behaviour simulation of bonded steel-concrete composite beams is presented. Finally, the proposed numerical model is validated through comparisons between numerical results and experiment data.

Design optimization of bonded steel-concrete composite beams

Bonded steel-concrete is one new type composite structure in civil engineering domain. Generally, for steel-concrete composite structures, the steel beam and the concrete are connected by means of shear connectors. This work consists in analyzing the design optimization of the steel-concrete composite beam connected by adhesives instead of metal connectors. The principal parameters, including elastic modulus of adhesive, the adhesive layer thickness, the bonding strength and the bonding area, which influence the mechanical behaviours of the bonded steel-concrete composite structures, have been investigated. Finally, an example of design optimization of a single span adhesive bonded steel-concrete composite beam is proposed.