An offline-online strategy for multiscale problems with random defects

In this paper, we propose an offline-online strategy based on the Localized Orthogonal Decomposition (LOD) method for elliptic multiscale problems with randomly perturbed diffusion coefficient. We consider a periodic deterministic coefficient with local defects that occur with probability $p$. The offline phase pre-computes entries to global LOD stiffness matrices on a single reference element (exploiting the periodicity) for a selection of defect configurations. Given a sample of the perturbed diffusion the corresponding LOD stiffness matrix is then computed by taking linear combinations of the pre-computed entries, in the online phase. Our computable error estimates show that this yields a good approximation of the solution for small $p$, which is illustrated by extensive numerical experiments. This makes the proposed technique attractive already for moderate sample sizes in a Monte Carlo simulation.

Planar Compliance Realization with Two 3-Joint Serial Manipulators Connected in Parallel

In this paper, the realization of any specified planar compliance with two 3R serial elastic mechanisms is addressed. Using the concepts of dual elastic mechanisms, it is shown that the realization of a compliant behavior with 2 serial mechanisms connected in parallel is equivalent to its realization with a 6-spring fully parallel mechanism. Since the spring axes of a 6-spring parallel mechanism indicate the geometry of a dual 3R serial mechanism, a new synthesis procedure for the realization of a stiffness matrix with a 6-spring parallel mechanism is first developed. Then, this result is extended to a geometric construction-based synthesis procedure for two 3-joint serial mechanisms.

On two simple virtual Kirchhoff-Love plate elements for isotropic and anisotropic materials

The virtual element method allows to revisit the construction of Kirchhoff-Love elements because the $$C^1$$ C 1 -continuity condition is much easier to handle in the VEM framework than in the traditional Finite Elements methodology. Here we study the two most simple VEM elements suitable for Kirchhoff-Love plates as stated in Brezzi and Marini (Comput Methods Appl Mech Eng 253:455–462, 2013). The formulation contains new ideas and different approaches for the stabilisation needed in a virtual element, including classic and energy stabilisations. An efficient stabilisation is crucial in the case of $$C^1$$ C 1 -continuous elements because the rank deficiency of the stiffness matrix associated to the projected part of the ansatz function is larger than for $$C^0$$ C 0 -continuous elements. This paper aims at providing engineering inside in how to construct simple and efficient virtual plate elements for isotropic and anisotropic materials and at comparing different possibilities for the stabilisation. Different examples and convergence studies discuss and demonstrate the accuracy of the resulting VEM elements. Finally, reduction of virtual plate elements to triangular and quadrilateral elements with 3 and 4 nodes, respectively, yields finite element like plate elements. It will be shown that these $$C^1$$ C 1 -continuous elements can be easily incorporated in legacy codes and demonstrate an efficiency and accuracy that is much higher than provided by traditional finite elements for thin plates.

Asymmetric Design Sensitivity and Isogeometric Shape Optimization Subject to Deformation-Dependent Loads

We present a design sensitivity analysis and isogeometric shape optimization with path-dependent loads belonging to non-conservative loads under the assumption of elastic bodies. Path-dependent loads are sometimes expressed as the follower forces, and these loads have characteristics that depend not only on the design area of the structure but also on the deformation. When such a deformation-dependent load is considered, an asymmetric load stiffness matrix (tangential operator) in the response region appears. In this paper, the load stiffness matrix is derived by linearizing the non-linear non-conservative load, and the geometrical non-linear structure is optimally designed in the total Lagrangian formulation using the isogeometric framework. In particular, since the deformation-dependent load changes according to the change and displacement of the design area, the isogeometric analysis has a significant influence on the accuracy of the sensitivity analysis and optimization results. Through several numerical examples, the applicability and superiority of the isogeometric analysis method were verified in optimizing the shape of the problem subject to deformation-dependent loads.

Stiffness matrix method for analysis of torsionally loaded piles in multi-layered soil

A new, simple, and practical method to investigate the response of torsionally loaded piles on homogeneous or non-homogeneous multi-layered elastic soil is developed. The soil non-homogeneity is accounted for by assuming for each layer a shear modulus distribution that fits a quadratic function. The analysis of piles in multi-layered soil is carried out by subdividing the pile, at the soil-soil layer and soil-air interfaces, into multiple elements, and then using conventional matrix methods -such as those commonly implemented in structural analysis- to connect them. The governing differential equation (GDE) of an individual structural element is solved using the Differential Transformation Method (DTM). Next, the stiffness matrix is derived by applying compatibility conditions at the ends of the element. Piles partially or fully embedded in multiple layers and subjected to torsion can be analyzed in a simple manner with the proposed formulation -a tedious endeavor with other available solutions. Finally, explicit expressions for the coefficients of the matrix are provided. Four examples are presented to show the simplicity, accuracy, and capabilities of the proposed formulation.

Distributed variable stiffness joint assist mechanism based on laminated structure

Exoskeleton technology is more and more widely used in military, human rehabilitation, and other fields, but exoskeleton assisting mechanisms have problems such as high quality, concentrated driving sources, and poor flexibility. This article proposes a distributed variable stiffness joint power-assisted mechanism based on a laminated structure, which uses a giant magnetostrictive material as the driving source and the variable stiffness source of the structure. The distributed driving is realized by multiple driving units connected in series and parallel. Firstly, the drive unit stiffness matrix is deduced, and the expression equations of the cascaded total stiffness matrix of the drive module are obtained. After the simulation study, the curve of the stiffness of a single drive unit with a magnetic field and the stiffness of multiple drive units connected in series and parallel are in the absence of the magnetic field. The change curve of the stiffness of the booster module with the number of drive units under the excitation and saturation magnetic field excitation conditions is to achieve the effect of dynamically controlling the structural stiffness of the drive unit by controlling the size of the magnetic field and to obtain a general formula through data fitting. The number of drive units required under a fixed magnetic field excitation can ensure that the error is within 5%. The research results lay the foundation for further analysis of the distributed variable stiffness joint assist technology.

Investigation on the influence of point loads on the deflection behaviour of G+5 frame structure

Nowadays, multi-storey structure portal frames are most commonly used worldwide. Multistory frames are used in structural systems in all metropolitan cities, future cities, and important businesses. The present study the effect of various point loads varying from 22 to 32 kN in steps of 2 were applied on the center of horizontal beams of the frame structure. The deflection behaviour in form of deflection, reaction, beading moments under point loading were discussed analytically according to stiffness matrix method and the results are validated with the help of simulation using STAAD Pro software. Results revealed that the analytical method using manual calculations in excel sheet provides approximately similar results as obtained by the costly simulation technique using STAAD Pro software. Therefore, the implementation of this excel sheet can be recommended for standard analysis of portal frame structures based on the outcomes of this study.