The main results of the study are obtained as follows:1 In order to analyze and study the physical and mechanical characteristics of Lianyungang marine soft clay deeply, large numbers of basic mechanical characteristics tests and tri-axial shear tests are completed.2 In order to investigate the loaded and failure characteristics of the cement-soil, the cement-soils for the different ratio and different cure time are studied in the laboratory, and their unconfined compression tests and tri-axial shear tests are performed.3 Based on the solution of one-dimension consolidation, the one-dimension consolidation of the double-layered foundation is solved for two-grade loading in virtue of transcendental equation; Simultaneously, the one-dimension consolidation of the double-layered foundation is solved by means of Laplace transform for two-grade loading, and Stehfest numerical transform is applied in Laplace`s inverse transformation; Furthermore, according to the practical foundation shapes, the consolidation models of the soil between piles and the substratum are built and solved respectively.4 The effect of each parameters on the consolidation of the double-layered foundation is discussed, and the solution of load transfer method for double-layered foundation is applied in A1-A4 section of Lian-Xu expressway. The results of calculating settlement of the double-layered consolidation theory are basic agreement with the measuring settlement results.
取得了以下几方面的研究成果：1针对连云港海相软土进行一维固结和三轴剪切试验，深入分析连云港海相软土的物理力学特性。2模拟水泥土搅拌桩施工，在室内制备不同配比、不同龄期的水泥土试样，并进行无侧限抗压试验和三轴剪切试验，揭示水泥土的受力特性及破坏特性。3运用超越方程，以双层地基一维固结解析解为基础，推导出二级加荷条件下双层地基的固结解析解；同时，通过荷载传递法并借助Laplace变换对双层地基的固结问题进行了数值求解；此外，根据实际的地基结构，建立了桩间土和下卧层的固结模型并分别进行求解分析。4分析探讨了双层地基中各参数对双层地基固结的影响程度，并运用荷载传递法的解答计算了连-徐高速公路A1-A4标水泥土搅拌桩处理段的六个断面，计算结果与实测数据有较好的一致性。
By means of Laplace transformation and its inverse transformation, analytical solutions are deduced for one-end-fixed pole, cantilever and uncompressible tube composed of VFD material.
本文还用Laplace变换及其逆变换，推导出了杆件、悬臂梁和不可压缩圆筒的理论解，并将其用于发动机药柱的响应分析。
By this, the REDUCE system can be used in operation and inverse operation of abstract operator, Laplace transformation and inverse transformation, solving differential equation, formula manipulation, and proposition verification eta.
使REDUCE系统可用于抽象的算符演算，逆演算；用于Laplace变换，逆变换及解微分方程，推导公式，以及验证有关定理等。
Based on the nature of Laplace transformation and inverse Laplace transformation, this paper introduces the additional function and obtains the concise analytical solution in the real space.
根据拉式变换及其逆变换的性质引入了附加函数，得到了形式简明的实空间上的解析解。
By using Fourier transformation for space variable, Laplace transformation for time variable and convolution theorem for their inverse transformations, a general solution for dynamical problem of infinite beam on an elastic foundation is obtained.
然后对空间变量和时间变量分别进行Fourier变换和Laplace变换，利用逆变换褶积积分，得到了弹性地基无限长梁一般动力问题的解析解。
The frequency domain transfer function of the thin metallic shell is fit into a rational function using the vector fitting method, with the pulse response expressed as a sum of decay exponentials in the time domain from the inverse Laplace transformation.
该方法将金属薄壳频域屏蔽效能转移函数拟合为有理函数，根据拉氏逆变换性质，得到金属薄壳脉冲时域响应指数叠加的形式，从而采用递归卷积计算任意波形激励时金属薄壳的暂态屏蔽效能。
With Laplace transformation and inverse Laplace transformation, analytical solutions of time domain response and frequency domain response of single degrees-of-freedom are obtained.
用Laplace变换及其反变换，解析地计算了解耦后单自由度系统的时域和频域响应。
A numerical method of inverse Laplace transformation of the fractional function
分式函数拉氏反变换的数值计算简法
By using the integral transform method, it is reduced to the solution of a singular integral equation of the Cauchy type in Laplace transform domain. Numerical computation was then performed and the inverse Laplace transformation carried out.
用积分变换法将问题化为一个在Laplace变换域内的Cauchy型奇异积分方程，然后求数值解，并完成Laplace逆变换。
Based on distribution parameter node admittance equations and the method of the numerical inverse Laplace transformation (NILT), crosstalk coupling voltage responses are analyzed at terminals of transmission lines with common ground.
基于传输线分布参数节点导纳方程和数值拉普拉斯反变换（NILT）方法，仿真分析了传输线串扰电压响应及传输线参数和端接阻抗对串扰电压峰值的影响。
Numerical results for several response modes such as breathing mode and translational mode were obtained by inverse Laplace transformation, and were used to discuss the influence of relative rigidity of liner and soil on the dynamic response of the tunnel.
利用Laplace数值逆变换在时间域中得到瞬时、移动等响应模式条件下的数值结果，并讨论了衬砌和土体的相对刚度对隧洞动力响应的影响。
Generalization and Application of Expansion Theorem of Inverse Laplace's Transformation
逆Laplace变换展开定理的推广和应用
The elasticity and cohesive-elasticity solution of surrounding rock is solved by corresponding principles and Laplace inverse transformation.
由弹性一粘弹性对应性原理及Laplace逆变换求得相应围岩的粘弹性解。
Effects of wellbore storage and skin factor on horizontal wellbore pressure were considered when the method of convolution integral, numerical Laplace transformation and numerical Laplace inverse transformation were used. It is not necessary to solve the mathematical model with complicated inner conditions.
采用Laplace数值变换、Laplace数值反演及褶积积分公式考虑了井储和污染对水平井井底压力的影响，从而避免了求解复杂内边界条件的数学模型的问题；
A Laplace inverse transformation of a random variable sequence of independent same exponential distribution
独立同指数分布的随机变量序列的一个Laplace反演变换
Laplace Inverse Transformation and Asymptotic Expansion for n-times Integrated C-semigroups
n次积分C半群的Laplace逆变换及渐近展开