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The Convolution Quadrature Method (CQM) has been widely applied to solve transient elastodynamic problems because of its stability and generality. However, the CQM suffers from the problems of huge memory requirement in case of direct implementation in time domain or CPU time in case of its reformulation in Laplace domain. The purpose of this paper is to combine the CQM with the pseudo-initial condition method (PICM) to achieve a good balance between memory requirement and CPU time.

The combined methods first subdivide the whole analysis into a few sub-analyses, which is dealt with the PICM, namely, the results obtained by previous sub-analysis are used as the initial conditions for the next sub-analysis. In each sub-analysis, the time interval is further discretized into a number of sub-steps and dealt with the CQM. For non-zero initial conditions, the pseudo-force method is used to transform them into equivalent body forces. The boundary face method is employed in the numerical implementation. Three examples are analyzed. Results are compared with analytical solutions or FEM results and the results of reformulated CQM.

Results demonstrate that the computation time and the storage requirement can be reduced significantly as compared to the CQM, by using the combined approach.

The combined methods can be successfully applied to the problems of long-time dynamic response, which requires a large amount of computer memory when CQM is applied, while preserving the CQM stability. If the number of time steps is high, then the accuracy of the proposed approach can be deteriorated because of the pseudo-force method.

The purpose of this paper is to develop a quantitative risk assessment method for agricultural products cold chain logistics to assess the condition of the fresh agricultural products cold chain process objectively and accurately.

A risk assessment index system of agricultural products cold chain logistics is designed on the basis of the risk identification for the process of agricultural products cold chain logistics. This paper first uses catastrophe progression method and a new maximum deviation method to build an improved catastrophe progression assessment model for agricultural products cold chain logistics. In order to verify the reliability and validity of the model, two representative enterprises are selected as the case in the study.

The results in the empirical research indicate strong support for the assessment model and coincide with the reality. The risk assessment index system can also reflect the key risk factors from agricultural products cold chain logistics scientifically. In addition, the improved catastrophe progression assessment method proposed in this paper can be scientific and reasonable to predict risk.

This paper contributes to provide a new risk assessment model for agricultural products cold chain logistics. The new model overcomes the limitation of subjective empowerment and it increases the objectivity and scientificity in the process of cold chain logistics risk assessment. This paper also shows that practitioners involved in the field of products cold chain logistics can manage the potential risk by a set of scientific methods for assessing the risk before the accident.

The paper provides a practical guideline to practitioners, especially for cold chain logistics managers, relevant management departments, and cold chain logistics management consultants. It is proved that the new risk assessment method and the risk assessment index system of agricultural products cold chain logistics can help them assess the risk scientifically and reasonably.

Although the calculation is simple, the new model can overcome the limitation of subjective empowerment scientifically and reasonably, and thus has important practical value.