線織面で構成されるラチスシェルの形状最適化

Various optimization problems have been studied for the purpose of structural morphogenesis by many researchers. Structural optimization problems can be classified into three different sub-problems, namely size, shape and topology optimization problem. Size optimization problem is consisted of small sets of design variables. The shape and topology of a structure are defined by a set of design variables, and these design variables are adjusted to achieve given objectives, such as minimum volume. Such optimization problems can be solved iteratively, using gradient-based techniques. Introducing more design variables increases the complexity of the optimization problem. Therefore, it becomes difficult to solve the optimization problem by using MP techniques with large sets of design variables. Heuristics can be improved the difficulty. There are many studies using heuristics like genetic algorithm and simulated annealing. An effective method for structural morphogenesis inspired by self-organization phenomena is presented in this paper. Self-organization is a phenomenon that an entire structure gradually emerges by interaction between elements of the structure, and the elements are affected by the entire structure. Since the self-organization algorithm consists of simple calculation iteration, it can be applied to problems with large number of design variables. Proposed method is applied to problems of uniform member length, minimization of strain energy and cross-section design for frame structures, and the effectiveness is demonstrated through some examples. On the other hand, the number of projects incorporating computational design has increased in recent year, and designs with complicated forms composed of free surfaces are also increasing. In order to design such a shape, the designer needs to consider the rationality of the structure from the initial stage. So, it seems necessary to develop simple software for the structural morphogenesis. Therefore, we developed components of Grasshopper that works within Rhinoceros, so that it will be possible to reassemble algorithms in an intuitive way for designers who have never experienced programming. Grasshopper is one of Graphical Algorithm Editor (GAE), and can be visually constructed an algorithm by connecting components that is a function of modeling. Analysis by gradient-based MP techniques often involves jumping of solutions and analytical instability peculiar to non-linear problems, and it is difficult to apply to the computer aided systems as described above. Analysis algorithms based on self-organizing algorithms are considered to be suitable for the above system due to their high robustness.

Effects of external trunk loads on lumbar spine stability

In engineering practice, longitudinal brace systems for column-braced systems are designed to resist both horizontal and vertical loads. In previous experimental research on horizontal brace forces for column-braced systems of intermediate height, only vertical loads were considered. Hence, this paper presents a numerical simulation of numerous column-braced systems subjected to horizontal and vertical loads. In the numerical simulation, second-order analysis was adopted, and the Monte Carlo method was used to incorporate the randomness of initial imperfections in the horizontal brace and column. From the finite element (FE) analyses and probability model statistics, the normal probability density equation for intermediate-height horizontal brace forces under horizontal and vertical loads was obtained, and the corresponding design intermediate-height horizontal brace forces were determined and compared with those under vertical loads only. The results indicate that the design intermediate-height horizontal brace forces under horizontal and vertical loads are significantly greater than those under only vertical loads, and that the design intermediate-height horizontal brace forces under horizontal and vertical loads are also greater than the simple superposition results of horizontal loads and intermediate-height horizontal brace forces under only vertical loads.

Shape optimization is a pervasive tool for designing concrete free-form shells. However, the existing shape optimization approaches for free-form shells usually assume the material is purely elastic without considering material damage, which may produce undesired results in real-world structural applications, especially in the case of concrete structures. In this article, a framework is presented for performing the shape optimization of concrete free-form shells while considering concrete damage. In the proposed optimization algorithm, the Mazars model is coupled with finite element analysis for modelling structural responses subjected to material damage. Through a series of numerical examples, the proposed algorithm is validated and the effects of material damage on optimal results are investigated. It is demonstrated that the consideration of material damage leads to a more robust design, which highlights the importance of accounting for the material damage during the shape optimization process of concrete free-form shells.

This paper presents design data defining optimal freeform notch shapes for use in tensile loading conditions for a range of geometries, notably the notch aspect ratio and plate widths. Here, an iterative two-dimensional finite element gradientless shape optimization procedure was used to obtain the optimal shapes, which offer the lowest possible stress concentration, subject to the geometric constraints. Precise non-dimensional coordinates are given, for a range of notch aspect ratios and plate widths, and are presented in a tabular form that allows them to be easily used by designers. All cases have been solved with a minimum radius of curvature constraint, which results in a ‘robust’ optimal shape that has no sharp corners. The optimal shapes were found to provide up to a 26 per cent reduction in local peak stress over circular shapes of the same aspect ratio. Optimal geometries are also given for limiting notches that provide a net section stress equal to unity, at a finite notch aspect ratio. The results obtained are applicable to both the initial design of notched components and the shape reworking of existing components to remove damage.

The present paper investigates the tailoring of bimaterial microstructures minimizing their local stress field exploiting shape optimization. The problem formulation relies on the extended finite element method (XFEM) combined with a level set representation of the geometry, to deal with complex microstructures and handle large shape modifications while working on fixed meshes. The homogenization theory, allowing extracting the behavior of periodic materials built from the repetition of a representative volume element (RVE), is applied to impose macroscopic strain fields and periodic boundary conditions to the RVE. Classical numerical homogenization techniques are adapted to the selected XFEM-level set framework. Following previous works by the authors on analytical sensitivity analysis (Noel et al. (2016)), the scope of the developed approach is extended to tackle the problem of stress objective or constraint functions. Finally, the method is illustrated by revisiting 2D classical shape optimization examples: finding the optimal shapes of single or multiple inclusions in a microstructure while minimizing its local stress field.

An improved marine predators algorithm for shape optimization of developable Ball surfaces

Shape optimization in laminated composite plates

Limit load space of rigid strip footing on sand slope subjected to combined eccentric and inclined loading

In this paper, we investigate short-duration solitary wave impacts on overhanging near-coast structures, which are represented here as rectangular blocks protruding out from a vertical wall. Wave transformation is computed for a variety of scenarios using the OpenFOAM variant IHFOAM. In agreement with previous studies, the largest pressures and loads occur when there is a violent impact with near-breaking or just-broken waves on the wall, causing a strong vertical jet. This condition most easily occurs with steep near-shore slopes. Maximum vertical loads on overhangs occur at significantly higher block elevations than are found for maximum horizontal loads. Overhang lengths have small effects on magnitudes of horizontal forces, but strongly increase positive uplift vertical loads. Although maximum instantaneous vertical loads can significantly exceed instantaneous horizontal loads, time-averaged vertical loads decrease rapidly with increasing averaging period while horizontal loads show more modest decreases; horizontal loads significantly exceed vertical loads for large averaging periods. This indicates that the pressure-impulse in the wall-generated vertical jets is much less than that arising from the horizontal solitary wave impacts.

Engineering structures consist of various components, and the components interact with each other through contact. Engineers tend to consider the interaction in analysis and design. Interactions of the components have nonlinearity because of the friction force and boundary conditions. Nonlinear analysis has been developed to accommodate the contact condition. However, structural optimization using nonlinear analysis is fairly expensive, and sensitivity information is difficult to calculate. Therefore, an efficient optimization method using nonlinear analysis is needed to consider the contact condition in design. Nonlinear Response Optimization using Equivalent Loads (NROEL) has been proposed for nonlinear response structural optimization. The method was originally developed for optimization problems considering geometric/material nonlinearities. The method is modified to consider the contact nonlinearity in this research. Equivalent loads are defined as the loads for linear analysis, which generate the same response field as that of nonlinear analysis. A nonlinear response optimization problem is converted to linear response optimization with equivalent loads. The modified NROEL is verified through three examples with contact conditions. Three structural examples using the finite element method are demonstrated. They are shape optimization with stress constraints, size optimization with stress/displacement constraints and topology optimization. Reasonable results are obtained in the optimization process.

Comparative analysis of moisture-dependent physical and mechanical properties of two varieties of African star apple (Chrysophyllum albidum) seeds relevant in engineering design

Strain energy anisotropy in germanium and other diamond-cubic polycrystalline films

This paper deals with shape optimization of three-dimensional elastic bodies. The proposed approach is based on natural design variables and shape functions and utilizes the boundary element method. The design variables are the magnitudes of a set of fictitious loads applied on the structure. Shape optimal design problems based on minimum mean compliance, peak stress minimization and stress constraints are considered. A general method for shape design sensitivity analysis using the material derivative concept and adjoint variable method is used. The sensitivity formula for a general stress constraint imposed over the optimized boundary is derived. Optimal shapes for three-dimensional problems are presented to show numerical applications.

The fractional dynamics equation of a viscoelastic two-member truss system, in which fractional derivative model introduced to simulate the materials’ characteristics, is proposed. The equilibrium paths under vertical loads, horizontal loads and combined loads are discussed respectively. The results show that: there are primary and secondary equilibrium paths under vertical and horizontal loads. Bifurcations will occur under combined loads and the ultimate bearing capacity of the system will reduce. The equilibrium paths became complex because of the horizontal disturbance, and the bigger of the horizontal disturbance the smaller of the system ultimate bearing capacity.