A physical packing sequence algorithm for the container loading problem with static mechanical equilibrium conditions

The container loading problem (CLP) is a combinatorial optimization problem for the spatial arrangement of cargo inside containers so as to maximize the usage of space. The algorithms for this problem are of limited practical applicability if real-world constraints are not considered, one of the most important of which is deemed to be stability. This paper addresses static stability, as opposed to dynamic stability, looking at the stability of the cargo during container loading. This paper proposes two algorithms. The first is a static stability algorithm based on static mechanical equilibrium conditions that can be used as a stability evaluation function embedded in CLP algorithms (e.g. constructive heuristics, metaheuristics). The second proposed algorithm is a physical packing sequence algorithm that, given a container loading arrangement, generates the actual sequence by which each box is placed inside the container, considering static stability and loading operation efficiency constraints.

Dynamic stability metrics for the container loading problem

The Container Loading Problem (CLP) literature has traditionally evaluated the dynamic stability of cargo by applying two metrics to box arrangements: the mean number of boxes supporting the items excluding those placed directly on the floor (M1) and the percentage of boxes with insufficient lateral support (M2). However, these metrics, that aim to be proxies for cargo stability during transportation, fail to translate real-world cargo conditions of dynamic stability. In this paper two new performance indicators are proposed to evaluate the dynamic stability of cargo arrangements: the number of fallen boxes (NFB) and the number of boxes within the Damage Boundary Curve fragility test (NB_DBC). Using 1500 solutions for well-known problem instances found in the literature, these new performance indicators are evaluated using a physics simulation tool (StableCargo), replacing the real-world transportation by a truck with a simulation of the dynamic behaviour of container loading arrangements. Two new dynamic stability metrics that can be integrated within any container loading algorithm are also proposed. The metrics are analytical models of the proposed stability performance indicators, computed by multiple linear regression. Pearson’s r correlation coefficient was used as an evaluation parameter for the performance of the models. The extensive computational results show that the proposed metrics are better proxies for dynamic stability in the CLP than the previous widely used metrics.

Estudo geotécnico dos solos do vale do Leça no âmbito de uma obra de requalificação portuária

A expansão da área ocupada pelo Porto de Leixões (Matosinhos e Leça da Palmeira), sobre solos muito compressíveis, de origem fluvial e marinha, leva a que seja necessário recorrer à engenharia para encontrar soluções adequadas à utilização de obras dos fins em vista. Assim, na zona do porto são muitos os projectos de engenharia civil/geotécnica executados nestes solos. Como exemplo, podem citar-se a Consolidação do Terrapleno e Construção dos Caminhos de Rolamento do Terminal de Contentores TC4S, a Reabilitação de um troço com 110m, do Cais Sul e do Cais Nascente da Doca nº 4 e a Construção da Portaria Principal do Porto de Leixões, todos no vale fóssil do rio Leça. São vastos os métodos a usar para o melhoramento destes solos, a colocação de colunas de brita, com o objectivo de reforçar o solo, aumentando a sua capacidade de carga e funcionando como drenos verticais, para solucionar o problema das deformações excessivas durante e após o final da obra, uma alternativa consiste em induzir a aceleração da consolidação da camada de solo mole, o uso de pré-carregamento e drenos verticais são usuais. Quando o tempo de concretização da obra exige que o aterro seja utilizado de imediato, uma solução viável é a colocação de estacas, que transferem o peso do aterro, ou parte dele, para camadas mais competentes. Também se pode proceder à retirada do solo original e substituí-lo por outro de qualidade superior. A mais recente técnica de melhoria de solos por injecção - jet grouting - é utilizada em diversas situações, incluindo obras provisórias e definitivas. O presente trabalho visa descrever, em função dos diversos factores, o comportamento do solo face aos vários métodos utilizados e os objectivos pretendidos que serão abordados no enquadramento empírico do trabalho.

A straightforward method to obtain the cohesive laws of bonded joints under mode I loading

A simple procedure to measure the cohesive laws of bonded joints under mode I loading using the double cantilever beam test is proposed. The method only requires recording the applied load–displacement data and measuring the crack opening displacement at its tip in the course of the experimental test. The strain energy release rate is obtained by a procedure involving the Timoshenko beam theory, the specimen’s compliance and the crack equivalent concept. Following the proposed approach the influence of the fracture process zone is taken into account which is fundamental for an accurate estimation of the failure process details. The cohesive law is obtained by differentiation of the strain energy release rate as a function of the crack opening displacement. The model was validated numerically considering three representative cohesive laws. Numerical simulations using finite element analysis including cohesive zone modeling were performed. The good agreement between the inputted and resulting laws for all the cases considered validates the model. An experimental confirmation was also performed by comparing the numerical and experimental load–displacement curves. The numerical load–displacement curves were obtained by adjusting typical cohesive laws to the ones measured experimentally following the proposed approach and using finite element analysis including cohesive zone modeling. Once again, good agreement was obtained in the comparisons thus demonstrating the good performance of the proposed methodology.